Event Probabilities and u.s. Departmem Impact Zones for Hazardous of Transportation Federal Railroad Materials Accidents on Administration Railroads
Office of Research and Development Washington DC 20590
P. Ranganath Nayak Donald B. Rosenfield John H. Hagopian
Arthur D. Lillie, Inc. Acorn Park Cambridge MA 02140
DOT/ FRA/ORD-83/ 20 November 1983 This document IS available to the Final Report public through the National Technical Information Service, Springfield, Virginia 22161. NOTICE
This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Govern ment assumes no iabfl ity for its contents or use 1 thereof.
NOTICE
The United States Government does not endorse prod ucts or man ufacturers. Trade or manufacturers' names appear herein solely because they are con sidered essential to the object of this report. Technical Report Documentation Page R .po,' No. Go" n .... n' Acc ,on No. Recip n'·. Co o 1. 2. •• ••• 3. •• t log No. DOT/FRA/ORD-83/20
4. Title ond SlIbti'le EVENT PROBABILITIES AND IMPACT ZONES FOR HAZARDOUS November 1983 P.,fo,... ,ng 0'90nllOllOn MATERIALS ACCIDENTS ON RAILROADS 6. Cod. DTS-73 P.,Io, ...ing O,goni lolion R.po,' No. - -- - 8. I-::--�A :---:o,I.:-:-1 ------� --f 7 II,h nath Nayak, Donald B. Ro senfield and . P. Ranga John H. Hagopian DOT-TSC-FRA-83-S P.,Iorming O,gonization Nom. and Wo,1o Un,' (TRAIS) 9. Add,en 10. No. Arthur D. Little, Inc .* RR219/R2309 Controct Gron' N Acorn Park 11. 0' o. DOT-TSC-1607 Cambridge MA 02140 T yp. R.po" ond Co".r.d 13. 01 P.,iod ��------1 Sponso,lng Agency Norn. and Add,... 12. Final Report U.S. Department of Transnortation Federal Railroad Administration June 1978 - Feb . 1981 Office of Research and Deve10 �ent Spon,o,ing Agency Cod. 14. Office of Rail Safetv· ResearC1r, RRD-10 Hashinaton DC 20590 5I1ppl.rn.nlo,yNol .. 1 S. U.S. Department of Transportation Research and Special Programs Administration *Under contract to : Transportation Sy stems Center Cambrid2e MA 02142 Ab."ocl 16.
Procedures are presented for evaluating the probability and impacts of hazardous mater ial accidents in ra il transportation . The significance of track class for accident frequencies and of train speed for accident severity is quantified. Spec ial attention is given to the analysis of track-caused accident s. Quantitative estima tes are provided of the amount of hazardous ma terial released per accident, as well as of the area affected by these releases. An error analysis is made of the various probabilities.
KeyWo,d. 17. 18. Dist,ib",ion S'o'.rnen' Railroads DOCUMENT IS AVAILABLE TO THE PUBLIC Hazardou s Ma terials THROUGH THE NATIONAL TECHNICAL Probabilit ies INFORMATION SERVICE. SPRINGFIELD. VIRGINIA. Risk Analysis 22161
Security .. ,.port) S.clI,i C 1 oui thi' poge) No. Pog.. 19. Clo ". lof 'hi I 20. 'Y I. (01 21. 01 22. P,ice UNCLASSIFIED UNCLASSIFIED 296
Form DOT F 1700.7 18-72) Reproduction of completed poge authorized .1 PREFACE
This report presents methods for the quantitative estimation of the risk associated with the transportation of hazardous materials by rail. The work was sponsored by the United States Depar tment of Tran sportation, Federal Railroad Administration (FRA) , Office of Research and Development , Washington, DC, and performed by Arthur D. Little, Inc . under contract DOT-TSC-1607 . The proj ect was monitored by the Transportation Systems Center (TSC) , Department of Transportation , Cambridge, Massachusetts.
The authors are grateful to Dr. Theodore S. G1ickman* of the Transpor tation Systems Center for his support and guidance in the course of their investigations. We also wish to acknowledge the extensive support provided by Mr . Paul Brenner of Arthur D. Little, Inc., and by our erstwhile colleague, Mrs. Antoinette Mu sser Brad1ey.** Finally, we wish to ment ion the exceptional job done by Mr . Hans Sachdeva in preparing this report for publication .
*Now at Virginia Polytechnic Institute and State University . **Now at Mitre Corporation .
iii METR�C C��VEIRSDON t=ACTORS
23 8 = Approximate Conversions to Metric Meaalres = Approximate Conversions from Metric Measures = - 22 Symbol When You Know Multiply by To Find Symbol � 21 Symbol When You Know Multiply by To Find Symbol - = 8 LENGTH 20 - = LENGTH � _ 19 mm millimeters 0.04 Inches In r centllNt.. 0.4 Inch.. In =--- em m 3.3 feet h In Incha centlmet.. 18 met.. -2.& em 7 metorl 1.1 h feet centimeters == m yerds yd 30 em E...- yardl 0.8 - km kilometers 0.6 mUe. ml yd meters m - 17 mil.. kllomet. 1.6 ... km rnI =--= = 16 AREA AREA 6 =---- 16 square centlm.t.r. 0.16 square inch.. = cm2 1.,2 Ina square Inches 6.6 square centimet.,. cml m2 squar. meter. 1.2 squarey.rdl yrJil
hi squar. f .. t squ.re meters _ _ krn2 square kilom.t.rs 0.4 squ.re mile, mi2 0.09 mI 14 yrJil squareyard. 0.8 squar. h. hac:la,.. 110.000 rn2, 2.& .cre. 1Nt.. mI = mP squaremila 2.6 IqUDre kilometers krn2 � 13 ecr.s 0.4 hecta,.. he 6 - = MASS (weight) = MASS (weight) 12
_:: 0.036 ounctl . oz ounctl =-- 11 ,,:em. 01 28 arams I _ Ikg kllogr.ms 2.2 pound, pounds 0.4& kiloarama kg -= Ib Ib _ t tonn .. 11000 kg' 1.1 short toni short toni tonn.. 0.8 • 4 10 (2000 Ib' VOLUME VOLUME - � 9
n, & ml milllllt.rs 0.03 fluid ounces 'I tIP teaspoo millilit.,. ml - = 8 01 tablespoons 1& lit.,. 2.1 pint' pt Tbsp mllliliterl ml 3 = I fl oz mllllllt.,. ml I liter, 1.06 quartl qt fluid ounctS 30 � 7 e cups 0.24 IIt.,1 lit.,. 0.26 ganons gal I I pt pinu 0.47 lit.,. ml cubic met.. 36 cubic feet hl I qt lit.rs � 6 ml cubic met.,. 1.3 cubicyards yd' quam 0.95 I gal 3.8 lit.r. _ IIII110nt I =--- h' cub f .. t 0.03 cublc m.t.. rnl 2 = 5 TEMPERATURE (exact) ydl cub.cyll� dl cublem.t.... 0.76 rnl =- 4 TEMPERATURE (exact) - == ----.,;= °C C.lsius 9/5lthen Fahrenh.it OF .dd t.mper.tur. - temper.tur. 32' =-- 3 OF F.hrenheit &19 (.har Cel.iul 0C - 1 tDm .ture subtracting t.mpel'llture =- OF pei- 2 OF 212 = 32 98.6 321 0 - -40 80 120 160 • • onl and ore oth.r convDrll m .. == 1 I " I I I I I I I I I I '" " I " 2001 I '1 In. - 2 fi4 em 'ullCtly' For UK! ...... ubi - I Iii140 iit i I ii i Unl Walght and Price -20 I 100 NBS Mlec:. PubL 288. .. of u..u,... $2.25 SO Catalog -40 0 20 60 80 inches _ _ 0C 37 0C ND. C13 10 286. em 40 TABLE OF CONTENTS
CHAPTER PAGE l. SUMMARY 1
2 . INTRODUCTION 4
A. OBJECTIVES 4 B. CONCEPTUAL BACKGROUND 7 C. APPROACH 8 D. DATA SOURCES: THEIR USES, AND LIMITATIONS 17 E. REFERENCES 18
3. ACCIDENT FREQUENCIES AND RATES 23
A. INTRODUCTION 23 B. CHOICE OF EXPLANATORY VARIABLES 23 C. CHOICE OF MEASURES OF ACCIDENT RATES 24 D. HISTORICAL ACCIDENT STATISTICS 31 E. HISTORICAL DATA ON ��OSURE 40 F. HISTORICAL ACCIDENT RATES 45 G. TRAIN ACCIDENT FREQUENCIES AND PROBABILITIES 47 H. REFERENCES 50
4. NUMBER OF CARS DERAILING 51
A. INTRODUCTION 51 B. YARD AND MAINLINE DERAILMENTS--ALL CAUSES 51 C. YARD AND MAINLINE DERAILMENTS DUE TO TRACK CAUSES 59 D. COLLISIONS 59 E. COLLISIONS WITHOUT DAMAGED CARS S9
5. PRESENCE OF HAZARDOUS-MATERIAL CARS IN TRAINS 63
A. INTRODUCTION 63 B. RATE OF OCCURRENCE OF HAZARDOUS-MATERIAL CARS 63 C. PROBABILITY THAT A RANDOM TRAIN CONTAINS HAZARDOUS- 64 MATERIAL CARS D. EXTRAPOLATION OF � AND P VALUES 66 H H
v TABLE OF CONTENTS (continued ) CHAPTER PAGE
6. NL�ER OF HAZARDOUS-MATERIAL CARS DERAILING 70
A. INTRODUCTION 70 B. GENERAL STATISTICAL FORMULAS 70 C. AND VARIANCE OF NUMBER OF HAZARDOUS-MATERIAL 71 MEANCARS DERAILING H D. FITTING A DISTRIBUTION TO T E MEANS AI.'ID VARIANCE 75 E. REFERENCES 79
7. RELEASE PROBABILITY 80
A. INTRODUCTION 80 B. DERAILMENTS 80 C. COLLISIONS 87
8. NUMBER OF HAZARDOUS-MATERIAL CARS RELEASING THEIR CONTENTS 89
A. INTRODUCTION 89 B. NUMBER OF HAZARDOUS-MATERIAL CARS RELEASING 89 C. VALUES FOR m AND k 91 r, G H D. QUANTITATIVE RESULTS FOR MEANS AND VARIANCES 94 E . REFERENCE 96
9. �'10UNT OF HAZARDOUS MATERIAL RELEASED : MEAN AND VARIANCE 97
A. INTRODUCTION 97 B. QUANTITY RELEASED PER CAR 97 C. ANOUNT RELEASED PER ACCIDENT 102 D. QUANTITATIVE RESULTS FOR MEANS AND VARIANCES 106 E. THE GAl-noIA-FITTING PROCEDURE 106
10. AMOUNT OF HAZARDOUS-MATERIAL RELEASED PER ACCIDENT: 112 DISTRIBUTION
A. INTRODUCTION 112 B. THE PROCEDURE 112 C. RESULTS 112 D. ACCURACY CHECK 117 E. APPLICATION OF PROCEDURE 117
11. ERROR ANALYSIS OF THE RISK ESTIMATES 121
A. INTRODUCTION 121 B. SOURCES OF ERROR 122 C. REVIEW OF RISK-ESTI�IATION PROCEDURE 123 D. QUANTITATIVE ERROR ESTI�TES 124
vi TABLE OF CONTENTS (continued) CHAPTER PAGE 12. AREA AFFECTED BY A RELEASE 134 A. INTRODUCTION 134 B. SELECTION OF HAZARDOUS-MATERIAL CATEGORIES 137 C. IDENTIFICATION OF FEASIBLE SCENARIOS AND 14 2 NECESSARY MODELS D. DAMAGE CRITERIA 147 E. SELECTION OF REPRESENTATIVE CHEMICALS: APPROACHES 160 TO IMPACT ASSESSMENT F. IMPACT-ASSESSMENT METHODS 171 G. SUMMARY OF IMPACT-ASSESSMENT RESULTS 173 H. REFERENCES 182
APPENDICES A. ANNOTATED BIBLIOGRAPHY A-1
B. MODELS FOR GENERATING PROBABILITY DISTRIBUTION FOR B-1 THE NUMBER OF CARS RELEASING AND THE AMOUNT RELEASED C. OVERVIEW OF HAZARD-ASSESSMENT MODELS C-1 D. APPLICATION OF HAZARD-ASSESSMENT MODELS D-1
vii LIST OF FIGURES
FIGURE PAGE 2-1 STRUCTURE OF THE MODEL FOR ANALYZING THE POTENTIAL 9 IMPACTS OF HAZARDOUS MATERIALS TRANSPORTED OVER A RAIL LINK 2-2 DATA SOURCES 22 3-1 INJURIES BY COMMODITY GROUP BASED ON RELEASES, 1971-1977 42 4-1 NUMBER OF CARS DERAILING: COMPARISON OF RECORDED AND 54 ESTIMATED SPEED 2 4-2 HISTORICAL VALUES OF and cr ESTIMATED FUNCTIONS 58 �_ N �� �D D 7-1 RELEASE PROBABILITY SHOWING RAW DATA AND ANALYTICAL 86 REPRESENTATION q(v),
9-1 MEAN �� VARIANCE OF AMOUNT RELEASED PER CAR 98 9- 2 DISTRIBUTION OF AMOUNT RELEASED AS A FUNCTION OF THE 101 NUMBER OF CARS RELEASING
10-1 CUMULATIVE DISTRIBUTIONS OF AMOUNT RELEASED, AR, GIVEN 113 THAT NH > O. ALL MAINLINE AND YARD COLLISIONS AND DERAIU1ENTS. ) (
10-2 CUMULATIVE DISTRIBUTIONS OF AMOUNT RELEASED , AR, GIVEN 114 THAT NH > O. (ALL TRACK-CAUSED MAINLINE AND YARD DERAILNENTS . ) 10-3 EFFECT OF TRACK CLASS ON THE CONDITIONAL DISTRIBUTION OF 115 AMOUNT RELEASED FOR MAINLINE DERAILMENTS 10-4 EFFECTS OF TRACK CLASS ON THE CONDITIONAL DISTRIBUTION OF 116 AHOUNT RELEASED FOR MAINLINE COLLISIONS 12-1 EVENT TREE FOR COMPRESSED GASES 146 12-2 EVENT TREE FOR LIQUIDS 148 12-3 HODEL UTILIZATION FLOWSHEET 149
viii LIST OF TABLES
TABLE
2-1 USES OF DATA SOURCES 19
2-2 SOURCES OF INFORMAXION FOR VARIOUS INDEPENDENT 20 VARIABLES AND MEASURES OF SEVERITY
2-3 PROBLENS IN FEDERAL RAILROAD ADMINISTRATION DATA 21
3-1 ACCIDENTS ON CL ASS 1 TRACK. (195- 7 1977) 32
3-2 ACCIDENTS ON CLASS 2 TRACK. (1975 19- 77) 33
3-3 ACCIDENTS ON CLASS 3 TRACK. (195- 7 1977) 34
3-4 ACCIDENTS ON CL ASS 4 TRACK. (1975 19- 77) 35
3-5 ACCIDENTS ON CLASS STRACK. (1975 19- 7)7 36
3-6 ACCIDENTS ON CL ASS 6 TRACK. (195- 7 197 7) 37
3-7 SUMMARY OF ACCIDENT DATA (195- 7 19 77) 38
3-8 MAINL INE ACCIDENT CAUSES (1975197 - 7) 39
3-9 COMPARISON OF DOLLAR DAMAGE R&�GES FOR HAZARDOUS- 41 MATERIAL COMMODITY GROUPS
3-10 MAINLINE EXPOSURE DATA 43
3-11 HISTORICAL MAINLINE DERAILMENT RATES 46
3-12 HISTORICAL MAINLINE COLLISION RATE S 48
MEANS AND ST ANDARD VARIATIONS OF NUMBER OF CARS 4-1 THE 52 DERAILING (DERAILMENTS DUE TO ALL CAUSES)
4-2 SIGNIFICANCE TESTS FOR DIFFERENCES IN THE MEANS AND 55 VARIANCES OF NUMBER OF CARS DERAILING AT VARIOUS SPEEDS FOR MAINLINE AND YARDS
ix LIST OF TABLES (con tinued) TABLE PAGE 4-3 t-mANS&�D STANDARDDEVIATIONS OF THE NUMBEROF CARS 57 DERAILING( DERAILMENTS DUE TO ALLCAUS ES) 4-4 MEANSAND STAN DARD DEVIATIONS OF TIlENUMBER OF CARS 60 ) DERAILING( TRACK-CAUSED DERAILMENTS 4-5 H 62 STAIN TISCOLLISTICS IONS FOR T E NUMBEROF CARS DERAILEDO R DAMAGED 5- 1 H H 65 MATEFRACTIONRIAL OF DERAILINGCARS T AT CONTAIN AZARDOUS 5- 2 RELATIONSHIP BETWEENP H ANDTRAIN SP EED 67 5-3 ESTCARRIMATEDYING HPROBABIAZARDOUSLITYMATERIALS THAT A TRAIN IN AN ACCIDENT IS 68 6-1 VALUES OF REGRESSION CONST��TS FOR ME��AND VARI��CE 73 OF ND 6- 2 5 MEAN VALUESOF v ANDva. 76 6-3 H 77 NillPERmE ACCIR OFDENT AZARD OUS-HATERIAL CARS DEkPILING OR DAMAGED 7-1 RELEASE PROBABILITY: DERAILMENTS (1975-197 7) 81 7- 2 RELEASE PROBABILITY: MAINLINE DERAILMENTS (1975-1977) 82 7-3 RELEASEPR OBABILITY: YARD DERAILMENTS (1975-1977) 83 7-4 5 H 85 FORRELEAS VARIOUSE PROB TRACKABILITY TYPECOMPA S RISON IN THE ° TO HP RANGE 7-5 RELEASE PROBABILITIES FOR COLLISIONS (1975-1977) 88 8-1 O 5 1. 5 2 92 MEANVALUES OF v . , v, v ANDv 8- 2 VALu�S OF REGRESSION CONST&�TS 93 8-3 PREDIRELEASCTEDING HEANTHEIRA.�D CONTENTS VARIANCE FOR TIlE NUMBEROF CARS 95
x LIST OF TABLES (continued)
TABLE PAGE
MEANS VARIANCES OF THE AMOUNT RELEASED PER CAR 9-1 AND 100 a FOR SELECTED VELOCITY CATEGORIES, IN GALLONS ( R) TESTS OF SIGNIFICANCE FOR VARIATIONS IN THE 9-2 MEAN AND 100 VARIANCE OF THE AMOUNT RELEASED PER CAR
9-3 VALUES OF VARIOUS REGRESSION CONSTANTS 104
9-4 MOMENTS OF THE DISTRIBUTION OF ACCIDENT SPEEDS 105
VARIANCE OF AMOUNT RELEASED PER ACCIDENT 9-5 MEAN AND THE 107
9-6 ESTIMATED PROBABILITY THAT A HAZARDOUS MATERIAL IS 111 RELEASED, GIVEN AN ACCIDENT
10-1 PROBABILITY THAT 0 GIVE N AN ACCIDENT WITH N 0 118 Aa = H > 10-2 COMPARISONS OF TABULATED RELEASE DISTRIBUTIONS GIVEN 119 . � > 0 FOR DERAILMENTS
11-1 UPPER AND LOWER BOUNDS FOR ACCIDENT RATES FOR VARIOUS 126 CLASSES OF TRACK: ALL MAINLINE DERAILMENTS
11 -2 UPPER AND LOWER BOUND ESTL�TES FOR ACCIDENT RATES FOR 127 VARIOUS CLASSES OF TRACK: TRACK-CAUSED MAINLINE DERAILMENTS
11 -3 UPPER AND LOWER BOUND ESTIMATES FOR ACCIDENTS FOR VARIOUS 128 CLASSES OF TRACK: MAINLINE COLLISIONS
UPPER LOWER BOUND ESTIMATES FOR ACCIDENT RATES IN 11 -4 AND 129 YARDS: DERAILMENTS COLLISIONS DUE TO ALL CAUSES Al�
UPPER LOWER BOUND ESTIMATES FOR THE CUMULATIVE 11 -5 AND 133 DISTRIBUTION OF THE AMOUNT RELEASED PER ACCIDE NT: ALL MAINLINE DERAILMENTS
12 -1 SUMMARY OF SELECTED HAZARDOUS-MATERIAL CATEGORIES 143
12 -2 RELATIVE COMPARISON OF HAZARDOUS-MATERIAL GROUPS BY 144 SEVERITY MEASURE
RELATIONSHIP BETWEEN PERCENTAGES 152 12 -3 AND Pr's
12-4 TOXIC VAPOR DAMAGE CRITERIA FOR THIRTY MINUTE EXPOSURE 159
xi LIST OF TA BLES (continued )
TABLE
12-5 S UMMARY OF PHYSICAL AGENT DAMAGE AND APPLICATION 161 CRI TE RIA
12-6 NON-FL AMMABLE CO MPRESSED GAS SPILL DA TA (1976) 164
12-7 DATA AN ALYSIS RESUL TS FOR NON-F L&�LE CO MPRESSED 165 GASES
12-8 IMPAC T ASSESS MENT RESULTS FOR NON-F LAMMABLE COMPRESSED 174 GASES
12-9 L�AC T ASS ESSMENT RESUL TS FOR FLAMMABLE CO MPRESSED GASES 176
12-10 IMPACT ASSESSMENT RESULTS FOR F LAMMABLE COMPRESSED 17 8 GASES
12-11 IMPAC T ASSESSMEN T RESULTS FOR F LAMMABLE COMPRESSED 179 GASES
12-1 2IMPAC T ASSESSMEN T RESULTS FOR FL AMMABLE COMPRESSED 180 GASES
12-13 IMPACT ASSESSMEN T RES ULTS FOR FL AMMABLE LI UIDS 181 Q 12-14 IMPACT ASSESSMENT RES ULTS FOR COMBUS TIBLE LI UIDS 183 Q 12-15 L�ACT ASSESSMENT FOR FL AMMABLE SOLIDS' SPECI AL HAZARD 184 ( ) 12-16 IMPACT ASSESSMEN T RESULTS FOR OXIDIZING MA ERIALS 185 T 12-17 IMPAC T ASSESS MENT RESULTS FOR ORGA4�IC PEROXIDES 186
12-18 IMPA C T ASSESSMENT RESUL TS FOR CLASS A POISON 187
12-19 IMPA C T ASSESSMEN T RESULTS FOR CLASS B POISON 188
12-20 IMPAC T ASSESSMENT RESUL TS FOR CORROSIVES 189
xii GLOSSARY OF SYMBOLS
Symbol Meaning a Amount of hazardous material released per car (gallons) R Amount of hazardous material released per accident (gallons) ACAa Accident cause AT Accident type d Regression constant for on v � D D Traffic density on a link e Regression constant for on v N a D E Exposure
E Number of events in collision rate model E(x) Expected value of x m = x f Regression constant for q on v F Frequency F * Statistic for significance testing g Regression constant for m on v G Gross tons per train � G H Group or block size for grouping of cars in trains h Regression constant for on v a HM Hazardous material � I Radiation intensity J Time integral of radiation intensity k Numb er of cars suffering a secondary release due to fire from a primary release
K Constant of proportionality between E and F for collisions L Link length Mean (or expected) value of x
Number of cars derailing in an accident Numbe� of hazardous material cars in a train Numb er of hazardous material cars derailing in an accident Number of hazardous material cars releasing their contents in an accident
xiii Symbol Meaning
Total number of ca rs in a train Probability distribution of x P{x) Pr obability of x P{T) Pressure as a function of time Percentage of a resource affected by aftermath of a release Probab ility of an accident Probab ility of an accident to a train carrying hazardous mater ial Conditional probability that a particular commodity is released given that on e of a group of commodities is released Probab il ity that at least one car is derailed or damaged in a collision P Probability that a train carries hazardous material H P Probab il ity of a re leas e given an accident R q Probability that a derailed hazardous material car will release its contents r Probab il ity of a secondary relea se , caused by fire from a primary release impinging on other cars t Time of exposure t Time of arrival of blast wave a t Time of passage of blast wave o TT Track type TC Track class v Train speed at time of accident (mph) Va r{x) Variance of x 02 = x x A random variable x y x given y y l A random variable Z Accident rate
xiv Symbol Meaning 2 Area within wh ich inj uries occur (km ) 2 aINJ Area within which severe irritation occurs (km ) CL1RR 2 Area within which le thal effects occur (km ) 2 aL Area within which property damage occurs (km )
Bap D Parameter for discretizing the continuous gamma distribut ion
� Constant of proportionality in collision analysis
A Parameter of the gamma distribut ion Parameter of the gamma distribution n Expected value of the ratio of to nH N N Standard deviation of x H T a x
xv/xvi I I
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I I 1. SUMMARY
This report presents methods for the quantitative estimation of the risk associated with the transportat ion of hazardous materials by rail.
Accident rates are developed separately for yard and mainline accidents . For each of these, derailments and collisions are treated separately . For dera ilments, track-caused accidents are also analyzed separately . Furthermore, for ma inline accidents , the effect of track class on accident rate is developed. Th is effect is found to be extremely important , as can be seen from the following tabulation.
Track Class 1 2 3 4 5&6
Mainline derailmen t rate ( �ccidents per 53 . 2 17.3 5.59 0.589 0.840 million gross ton- miles)
The empirically developed rate for Classes 5 and 6 (which were combined because of a lack of data for Class 6) is considered to be an anomaly , resulting from either a small sample size, or mis-reporting of track class , or errors in the estimation of the number of gross ton-miles for these two classes of track. The true rate for Classes 5 and 6 is almost certainly less than the rate for Class 4.
The severity of an accident , as defined by the number of cars derail ing or damaged , is found to be strongly depend ent on the speed at which the accident takes place. For derailments, the mean number of derailing cars, , is found to be: �D 0. 5 = 1 • 7 v , (1-1 )
1 where v is the train speed in miles per hour . The variance of the number of cars derailing is found to be:
= 2.7 v. (1-2)
The distribution of train speed varies significantly from one track class to ano ther. The mean speeds for mainline derailments are given in the following tabulation :
Track Class 1 2 3 4 5&6
Average train speed 8. 0 14 .9 21.3 29.7 37.6 (mph)
Thus , the average accident severity increases as track class increases.
A similarly strong dependence on speed is found fo r the probabil ity of release, q, which is the probability that a derailed hazardous ma terial car will release all or part of its contents . For all accidents, the following expression provides a good approximation to q:
q = (1-3)
Furthermore, the mean amount of material released from a car that does release also depends on the spee d:
(1-4) wh ere m is the mean value of the amount released per car gallons) . a (in R Thus , speed is seen to have a three-fold effect on the hazardous impact of an aCCident. As speed increases :
1. Thenu mb er of cars derailing increases, thus increasing the probability that hazardous material cars present in th e train will derail .
2 2 2. The probab il ity that a derailed hazardous material car tv.l11 release its contents increases .
3. The amount released from a releasing car increases.
Th e report provides rigorous analytical models for analyzing these effects , as well as quantitative results , leading to probability distributions for the total amount released in an accident , . These � are presented in Chapter 10.
Th e final step in the analys is procedure is to estimate the impacts on people and property of the accidental release of hazardous material. These impacts are estimated in terms of the area surrounding the site of the accident within which one or more of th e following impacts may be expected:
• fatalities,
• injuries,
• severe irritation, or
• property damage . Th e impacts are found to be strongly dependent on the total amount
released, AR' as well as on the type of hazardous material that is released. Estimates of these impacts are presented in Chapter 12.
Among the maj or contributions of this report ar e the rigor with which data was analyzed; the innovative models that were developed of the behav ior of a train in an accident; the quan titat ive analysis of the effects of track class and of train speed; the quantitative analysis of the effects of track-caused accidents; and the development of confidence bounds or error estimates for th e various probab ilities .
3 2. INTRODUCTION
A. OBJECTIVES
This report presents the results of work performed by Arthur D.
Little, Inc. , for the Transportation Systems Center (TSC) of the u.s. Department of Transportation (DOT) under Contract Number DOT-TSC-l607 . The objective of this work was to develop analytical techniques for assessing the risk involved in the transportation of hazardous ma terials (HM) on the network of u.S. railroads . Specifically , the contract called for three tasks to be performed :
1 . The development of probability distributions for the severity of hazardous-material accidents in rail transportation , aggregated over all possible' causes of accidents .
Due consideration was to be given to the basis for measuring accident rates (e.g. , ton-miles , car-miles, or train-miles); the definition of severity; important factors controlling the desired probability distribu tion; intended use of these distributions by TSC ; and also the methods by which traffic flow estimates were to be developed by TSC.
Specific thought was to be given to the use of statis tical techniques and analytical models for enriching what was expected to be a relatively sparse historical record and which would not, therefore, be a firm basis for direct extrapolation into the future.
2. The development of probability distributions similar to those developed in Task 1 with attention, in this case, confined to track-caused accidents.
3. The development of accident impact models which , given that an accident of specified severity had occurred , could be used to estimate the magnitude of the impact on the people and their property in the vicinity of the accident.
4 In this task, consideration was to be given to the nature of the hazardous material being released; methods by which traffic flow estima tes were to be obtained; and to the need for grouping hazardous materials (when ap propriate) to simplify the application of the models .
In planning the study, certain objectives were defined ; viz., that the effects on risk of at least the following variables ought to be quantified :
1. Thecon dition of the track over which the hazardous materials are being transported ;
2. The speed at which the transport occurs;
3. The nature of the hazardous material being transported ;
4. The quantity of hazardous material being transported in a typical train; and
5. The presence of classification yards en route, through which the hazardous materials must pass.
The effect of route-dependent characteristics, such as population density and property density, were to be accounted for separately , by superposing demographic statistics on the Federal Railroad Administration (FRA) Network Model [1 ].*
With the achievement of these objectives, as reported herein, it is possible to examine several aspects of risk-identification and reduction, of which the following are representative:
1. Identification of high-risk areas in the country;
2. Speed reduction for trains carrying hazardous materials ;
3. Improvements in track quality;
4. Re-routing of trains to avoid poor-quality track;
5. Re-routing of trains to avoid areas of dense population;
6. Use of through trains to avoid classification yards; and
7. Changes in train consists, such as the use of unit trains of hazardous materials.
* See References at the end of this Chapter .
5 It is also conceptually straightforward , using the methods presented herein, to forecast future risk(s) , taking into account possible changes in the flow of hazardous materials , demographic shifts, track deterioration or upgrading, as well as changes such as limits to tank capacity or the installation of head or thermal shields on tank cars.
The capabilities of the analytical models presented herein may be compared with the results of recent parallel work conducted elsewhere . Work sponsored by the Department of Energy (DOE) at Battelle [2,3] has con- centrated on the broad issue of the transportation risk arising from the consumption of materials important in energy production. The rail transportation portion of these studies [3] has concentrated heavily on risk-reduction measures associated with tank-car redesign, whereas in the study documented in this report , these possibilities were inten tionally ignored .
On the other hand , the Battelle work does not address the analysis of risk-reduction options involving changes in train make-up , speed , track upgrading, or routing , which are the focus of the Arthur D. Little study . It is worth noting that the results of the analysis of risk reduction redesign obtained by Battelle [3] can be introduced into the Arthur D. Little approach via a change in certain empirical 'para meters. A further interesting aspect of the Battelle work is the analysis of evacuation subsequent to a release of hazardous material . This is certainly an important factor in risk analysis , and is a useful complement to the work in the present report.
This study also sought to overcome certain deficiencies in other earlier analyses of the transport of hazardous materials by rail , a representative sample of which is cited in the Bibliography in Appendix A. The differences :
1. These studies are often concerned with qualitative methodology rather than with quantitative analysis of risk.
6 2. The models they use are generally applicable to one specific hazardous material or another.
3. The techniques were not suited to a nationwide analysis of risk, this being an important obj ective for the Transportation Systems Center, since it was , and is , its intention to use the FRA's Railroad Network Model to conduct a computerized , nationwide risk analysis.
B. CONCEPTUAL BACKGROUND
Any analysis, whether statistical or theoretical , must be based on a conceptual model , which then defines the kinds of questions that are to be asked and the types of analyses to be made. Within any given conceptual analysis, one approach to the analysis varies from another , not in any fundamental sense, but in the extent to which it relies on historical data as opposed to a theoretical model.
The conceptual �odel underlying the analyses presented in this report is based on certain observations and goals:
1. The harmful exposure of people or property to a hazardous material requires a series of events in an event chain. Each event is probabilistic, in the sense that its occurrence is not certain, given that the prior event in the chain has taken place: one can only assign a probability to its occurrence. This is also true of the first event in the chain, the occurrence of a train accident .
2. Many factors determine the conditional probability of an event, which is the probability that it will occur; given the condition that the prior event in the chain has occurred . These factors must be taken into account.
3. Several aspects of the event chain are common to accidents that do and do not involve hazardous materials . For example, it is likely that on a given class of track and in the absence of any special rules, the speeds at which trains travel on a given segment of track are independent of whether they carry hazardous materials or not. (Despite the recommendation by the Association of American Railroads that trains carrying DOT 112 and DOT 114 tank cars be(AAR) slo wed down by 10 miles per hour (mph) , the historical record of accidents does no t indicate that trains carrying tank cars operate at lower speed s than other trains .)
7 As another example, the number of cars that derail when a train derails may depend on such factors as the speed of derailment or the number of cars in the train, but the number is not likely to depend on-whether or not the cars carry hazardous materials. This observation is parti cularly important , since it justifies the use of a much larger set of data--all accidents--in modeling those portions of the event chain that are not influenced by the presence of hazardous materials .
4. The model must do more than fit past experience accurately; it must provide a basis for analyzing future conditions that have not occurred in the past , and also for.estimating the probability of occurrence of unusually severe incidents . Such catastrophic events may not have occurred in the past, partly because their probability of occurrence is low, and partly because the history of large movements of hazardous materials is a relatively recent one .
C. APPROACH
1. Overview
Figure 2-1 shows the approach to modeling that was used. The events in the chain are most easily described by grouping them into three maj or categories :
1. The occurrence of a train accident;
2. The occurrence of a hazardous-material release, conditional upon a train accident having occurred ; and
3. The impact upon people and property of hazardous materials , conditional upon a release having occurred.
Each of these segments is discussed separately in the following paragraphs.
2. Train Accident Rates and Freguencies
A train accident (or "rail equipment accident/incident") is defined [4] as "any collision, derailment , fire, explosion , act of God , or other event involving operation of railroad on-track equipment (standing or moving) , which results in more than $1,750 in damages to railroad on track equipment , signals, track, track structure , and roadbed ."
8 E T DATA EV N CALCULATION INPUT
( Treck Class Accident Rate • Track Type (Yard. Main) • Type of Accident ) •
TRAIN I Traffic Density • ACCIDENT Accident Frequency Trip Length • ) Number of Yards J • "
Probability Distribution of Number of Cars Derailing Speed or Track Class • Given an Accident
,
Ratio of hazardous-material , • to total number of cars Probability Distribution of cars Probability that a random Number of Hazardous- • Material Cars Derailing , train carries hazardous material cars (empirical)
,
Probability Distribution of Number of Cars Releasing Speed or Track Class • Their Contents
,
, RELEASE OF Probability Distribution of Speed or Track Class • HAZARDOUS Amount of Hazardous Empirical distribution of • MATERIAL Material Released amount released per car
IMPACT ON Probability Distribution of I Type of hazardous material PEOPLE AND Area Exposed to Harm \ • Locale: urban or rural PROPERTY - Lethal to humans • ) - Property damage ,
FIGURE 2-1. STRUCTURE OF THE MODEL FOR ANALYZING TH E POTENTIAL IMPACTS OF HAZARDOUS MATERIALS TRANSPORTED OVER A RAIL LINK
9 The threshold of $1 ,750 has been gradually increased since 1977 to account for the effects of inflation .
The accident frequency for a link in a railroad network is stated in terms of the expected number of accidents per year. This frequency depends on the exposure on that link and on the accident!!!! . For example, the rate for derailments might be stated in the expected number of accidents per gross ton-mile (GTM) ; the complementary measure of exposure on a link is then the GTM per year .
The rate of train accidents depends on certain significant factors , each of which is described below.
1. The type of track determines the appropriate measure of exposure and , therefore, the accident rate. There are four generic track types used by the FRA [4] in its accident reporting system; viz. , mainline , yard , siding , and industry. This report is confined to an analysis of mainline and yard accidents. The inclusion of siding and industry track accidents would have substantially compli cated the models t..rithout significantly improving the accuracy of the analysis of risk.
2. For mainline accidents, the class of track [5] is shown to be an important determinant of accident rates . While the true underlying variable is track quality , it is no t yet known how quality is to be defined and measured . Track class was therefore used as a surrogate for track qua�ity. In making this approximation, it is important to note that true track quality may vary widely within a given track class. See Chapter 11, Section B.
3. The type of accident obviously affects the accident rate. The measure of exposure for derailments is different from that for collisions , and the rates are therefore different . The FRA [4] classifies accidents into 11 different types , of which only the most important types are included in this report : derailments and collisions of all types. These two accident types a ccount for more than 90 percent of all acc idents , and for a similar proportion of the risk from hazardous materials transportation.
4. Accidents can be grouped according to their cause; rates then depend on the cause. For this study, two broad groups of causes were used : "all causes" and "track causes ."
10 The rate of accidents may also depend on other factors, such as train speed and make-up, variations 'of true track quality wi thin a given track class (such as might reflect variations from one railroad to ano ther) , or weather conditions. Although these other factors were examined in detail, it was not found to be feasible to include them in the model either because supporting data were unavailable, or because future users of the model would not have access to information regarding these factors.
Estimates of accident rates were made purely on the basis of historical statistics, with the exception that in the choice of a basis for measuring accident rates (the gross ton-mile was eventually chosen for derailments) , analytical reasoning was employed. The basis of this choice of a measure of "exposure," as well as the accident rates
determined from historical data, are presented in Chapter 3. Once the accident rate is known and the exposure on a rail link is specified , the expected frequency of accidents can be determined by mu ltiplying the two together. The frequency can either be stated on a temporal basis (per year) or on a traffic basis (per million gross tons or MGT) .
In summary, the first step determines the expected frequency of accidents:
= Z(TT, TC, AT , AC) . E (2-1) � where
= mean value of F, � F = frequency of accidents,
Z = accident rate,
TT = type of track,
TC = track class,
AT = accident type,
AC = accident cause, and
E = exposure.
11 Note that the appropriate measure of the exposure E, and therefore of the accident rate Z, depends on both the "type of track" variable , TT , and the "type of accident variable," AT , as shown at greater length in Chapter 3.
3. Hazardous Materials Release Given an Accident
If an accident occurs and its characteristics (such as track class , track type, etc.) are known, one may derive the probability distribution of the amount of hazardous material released in the accident as follows .
The conditional probability that the train contains hazardous material is first obtained . It is denoted by:
P (TT, AT , AC) . H rc, Then the conditional probability distribution for the number of cars derailing is obtained . It is represented by :
where Nn is the number of cars derailing and v is the speed at which the accident occurs.
Next the ?robability distribution of the number of hazardous material cars derailing , N , which is conditional on the number of cars HD derailing , is obtained. It has an ad ditional parameter, rrH, the proportion of hazardous-material cars to all cars. The cond itional distribution is deno ted by:
Then , the probability distribution of the number of cars releasing their contents , conditional on the number of hazardous-material cars derailing , is obtained :
12 In this expression, q is the release probability, which is a function of the speed at which the accident occurs and is thus written q(v) .
The probability distribution of the total amount of hazardous material released , is then found . It is denoted by: �, p( N , v) . R Aa! 4. Impact Given a Hazardous Material Release
Finally, the area within which lethal effects will be felt by human beings , denoted by aL, is shown as a deterministic function of the amount of hazardous material released, conditional on the type of material that is released :
where HM designates the hazardous material. Similar impact areas exist for injurious or irritating effects on people and for property damage , and are denoted by:
The expected impact area is estimated for several groups of chemicals and for each of the types of impacts listed above. The development of these estimates presented a considerable challenge, since the need for relatively simple results that could be used in a nation wide risk analysis conflicted with the known complexity of the phenomena that can occur after the release of certain hazardous materials. This conflict was resolved by taking the following steps:
• The various hazardous materials were grouped into a relatively small set of categories , based on their physical and chemical properties, including the types of phenomena that have been observed to occur upon their release .
• Two specific chemicals were chosen to represent each category: a "representative" one and a "worst-case" one.
13 When necessary , reasonable assumptions were made • regarding the probability of occurrence of competing post-release scenarios. Examples of competing scenarios, for a compressed flammable gas , include: a torch fire; a pool fire; a boiling liquid expanding vapor explosion (BLEVE) combined with one of the above two ; a vapor cloud fire; a vapor cloud deto nation; and a vapor cloud that disperses without igniting . Reasonable estimates were made of the input parameters • required by many of the impact models for the various scenarios. Examples of these parameters are the stability condition of the atmosphere, the wind velocity, and the density of ignition sources. The procedures used in applying these four steps are described in subsequent chapters, as are the results . The underlying models are described in Appendix C.
5. Synthesis All of these probability distributions are synthesized as follows :
1. Given an accident characterized by TT, TC , AT, and AC, the probability that the train carries hazardous material is PH' 2. Given an accident a train carrying hazardous material, as well as TT, TC, ofAT, and AC, the probability distribution for the lethal area is:
p(a I TT, TC, AT , AC, N 0, HM) L H > =
v x �P(�INR' v) aL(�IHM) d� dv. (2-2) �
In this expression, NH is the number of hazardous-material cars in the train, and
14 p(v TT, TC, AT, AC) I is the conditional probability distribution for the speed at which an accident occurs , given the various accident characteristics of TT , TC, AT , and AC.
An equation similar to (2-2) holds for the areas of inj ury or property damage ar and apD• Equation (2-2) is the central result of this report; the rest of the report is concerned with either developing approximate versions of it or with estimating th e conditional probability distributions that occur within it .
The subsequent analyses in this report first show:
Next , both
and
are shown , the latter being derived by combining the former with the conditional probability distribution for accident speed ,
p(v TT, TC, AT, AC) . I Here , in addition to the distribution of accident speeds, the historical dependence of � on TT, TC, AT , and AC is taken into account . H
Finally, both
and I p(N !T, TC, AT , AC , N > 0) R I H \� 15 are presented, as are:
p( N v), R' �I and
p( TT, TC, AT, AC, N 0) . �I H > In each case, the second distribution, which is conditioned by the track type, track class, accident type, and accident cause, assumes historical values for important parameters. The other less restrictive versions of the probability distributions allow the user to insert arbitrary values of these parameters .
6. Application
Equation (2-2) was applied in three di f ferent ways . One approach was aimed at determining the mean and variance of the probability distribution of A , and gaining approximate idea of the shape of R dn the overall distribution . In this approach, many of the intermediate probability dis tributions described above are no t explicitly derived, nor are they necessary. Only the mean and variance of each distri bution are necessary .
The second approach involved the use of actual historical distri butions of the amount released per car in combination with the means and variances of the number of cars releasing, to obtain explicit distributions for the total amount released . The advantages of this approach are that the distributions themselves are obtained rather than just their parameters .
The third approach involved the development of a mathematical representation of a train consist, aimed at developing analytical estimates of the number of hazardous-material cars derailing (N ), HO given the total number of cars derailing (N ). The approach then uses n historical data to obtain distributions of the number of cars releasing (N ), given N and the amount released given N • This approach R HD (�), R allows one to examine specific policy alternatives not otherwise
16 i f I amenable to analysis . An example of such a policy is a rule specifying a limit to the number of hazardous-material cars that may be carried in a train. The disadvantage of this approach is that the associated computational techniques are complex and ill-suited to the requirements of a nationwide or regional risk analysis. For this reason, this approach was not exercised to any great extent, except to make a brief comparison of its results with those of the other approaches described above.
For the sake of brevity, the analysis approach that estimates means and variances (parameters of probability distributions) is described as being based on "parameter models ." The second approach is described as being based on "distribution models ." The third approach is described as computer-based since the use of a computer is essential in its application.
D. DATA SOURCES : THEIR USES , AND LIMITATIONS
To develop and calibrate the models described in Section C, several sources of information had to be utilized:
1. The FRA Railroad Accident/Incident Report System (RAIRS) ;
2. The Materials Transportation Bureau incident (MTB) reports;
3. The National Transportation Safety Board (NTSB) investigations ;
4. The Association of American Railroads (AAR) and Railway Progress Institute (RPI) Tank Car Safety Research and Test Proj ect reports ;
5. Information contained in state rail plans ; and
6. Work on estimating flows of commodities , including hazardous materials , on the links of the FRA Network Model , being done at Princeton University [11·
17 The uses to \ihich the FRA and MTB data sources were put are summarized in Table 2-1 , and shown somewhat more explicitly in Table 2-2. Several problems were encountered in the quantitative analysis of the FRA/RAIRS and �lTB data, examples of which are sho\vo in Tab le 2-3 and Figure 2-2. A considerable amount of effort was expend ed in overcoming thesepr oblems and limitations . However, in the interest of brevity , the techniques used are not described in this report.
With reference to Figure 2-2 , it is particularly worth no ting that even wh en FRA and MTB records can be found for the same accident, the estimates of impact are not comparable. Th e FRA estimates include the numb er of cars releasing (but no t the amount of hazardous material released) , as well as the number of people killed or inj ured or the dollar damage to property due to all caus es. The MTB estimates include the amount releas ed , as well as the impacts on people and property--but only if they were caus ed specifically by the releas e of hazardous materials , and not by other consequences of the train wreck .
E. REFERENCES
1. "Federal Railroad Administration Network Mo del," Volume 1 (User I s Manual) , Report prepared by IBM Federal System Division , May 1975.
2. Andrews, t.r. B. , "An Assessment of the Risk of Transporting Liquid Chlorine by Rail ," Report No . PNL-3376, March 1980.
3. Ge ffen , C. E. , "An Assessment of the Risk of Transporting Propane by Truck and Train," Report No. PNL-3308 , March 1980.
4. "FRA Guide for Preparing Accident/Incident Reports," Federal Railroad Administration, 1975 .
S. Code of Federal Regulations , Title 49 , Part 213, "Track Safety Standards ," 19 77.
18 TABLE 2-1. USES OF DATA SOURCES
1. Determining 'Exposure' by Track Class:
• FRA/N e twork
• Princeton
• State Rail Plans 2. Modeling Train Accidents
• FRA/RAIRS 3. Mo deling Hazmat Train Accidents
• FRA /RAIRS
• MTB
• NTSB
• MIR/RPI 4. Modeling Impac ts
• MTB Prior Investigations •
19 TABLE 2-2 . SOURCES OF INFORMATION FOR VARIOUS INDEPENDENT VARIABLES &�D MEASURES OF SEVERITY
DATA SOURCES
INDEPENDENT VARIABLES FRA MTB
Flows
Accident Type .; Commodity " Track Class .; Speed " Track Type .; Cause .;
DATA SOURCES
SEVERITY MEASURES FRA MTB
$ Damages .; .; No. Killed " .; No . Inj ured .; .; No . Evacuated .; No. Hazmat Cars Derailing .; No. Hazmat Cars Releasing .; .; Quantity of Hazmat Released .;
, 20 "
II I I , I TABLE 2-3 . PROBL��S IN FEDERAL RAILROAD ADMINISTRATION DATA
• Occasionally }Iissing Information --Speed --Track class --Track density --Track data -No . of cars -No. of cars derailing -1st car position
• Multiple Reports --Up to seven --Difficult to automatically identify joint code date/time searches --Duplicat ion of -Damages -Killed -Injured -Cars on train -Cars derailing
Hazardous Material Not Identif ied •
21 Damage Threshold Damage Threshold • > • > No$ Release Hazm$ at Release • •
FRA DATA FRA MTB DATA & AVAILABLE AVAILABLE
FRA REPORTING THRESHOLD FOR DAMAGE
Damage Threshold Damage Threshold • < • < $No Release $ • • Hazmat Release
NO INFO RMATION MTB DATA SOURCE AVAILABLE
QUANTITY OF HAZARDOUS MATERIAL o RELEASED
FIGURE 2-2. DATA SOURCES
22 3. ACCIDENT FREQUENCIES A.� RATES
A. INTRODUCTION
This chapter presents historical data on accident rates and frequencies . Analyses that provide a useful perspective of the problem of railroad safety in general and of hazardous-material transport in particular are also presented .
Three maj or sources of information were used in developing the data presented here. Accident data were obtained largely from the Federal ., Railroad Administration's (FRA's) Railroad Accident/Incident Reporting 1 System (RAIRS) . Data for 1975, 1976, and 1977 are used . Data prior to 1975 contained less information on hazardous-ma terial (HM) accidents; data for 1978 and subsequent years were no t available at the start of this work.
Information on the total number of releases of hazardous material , the nature of the material released , and the quantity released per car and per accident were obtained from the �lateria1s Transportation Bureau 's (MTB 's) data for the years 1971 through 1977 . Data on flows , such as car miles and. ton-miles , were estimated by the Transportation Systems Center (TSC) and provided to Arthur D. Little, Inc .
Several other minor sources of information were also used , and these are cited where appropriate.
B. CHOICE OF EXPLANATORY V.�IABLES
A "model" for railroad accidents consists of a choice of expla natory variables that are thought to influence or determine the rate at which accidents happen, as well as their severity, and of an explicit relationship bet�l7een variables to be predicted (such as accident frequencies and severities) and the a� p1anatory variables . The relationship might be ob tained purely by curve-fitting of historical data, by theoretical modeling , or by a combination of the two .
23 As one's knowledge of railroad operations increases , it becomes ev ident that there are a host of factors that are important in accident analyses . However, the requirements of a large-scale safety study can be such that many of these factors have to be ignored , for one or more of the following reasons :
1. Data regarding the factors are not available;
2. The additional accuracy gained by including a factor does not justify its inclusion; or
3. The factor is important only for a small portion of all accidents .
On the basis of these qualitative criteria, several important choices were made in this study concerning variables to be included in the study of accident rates . These choices are briefly discussed below.
• Accident Location: Accidents are analyzed according to whether they occur on a mainline or in yards . Accidents occuring on sidings or on industry track are not included , as discussed in Chapter II .
• Accident Types : Two key accident groups are collisions (head-on and rear-end only) and derailments .
• Accident Causes : Track-caused accid ents are analyzed separately ; otherwise, there is no disaggregation of accidents according to their cause.
• Track Conditions : Track classification is accounted for in the analysis of mainline accidents; track quality variations within a track class are not .
C. CHOICE OF MEASURES OF ACCIDENT RATES
In any industrial activity , it is to be expected that the number of acc idents that occur in a fixed period of time will increase as the level of activity increases. It is commonplace, therefore, to measure safety not by the number of accidents that occur in a year (i.e. , by a frequency), but by an accident rate. An accident rate is simply the number of accidents divided by an appropriate quantitative measure of the level of
24 industrial activity . For many industrial accidents, rates are defined as accidents per man-hour . In another example--passenger transportation--the rate most often used is the number of accidents per passenger-mile. The use of such rates is essential , for the purposes of both comparison and prediction . As an example, no useful comparison can be made on the basis of the following hypothetical statement :
Ra,U,'toa.d A had 500 acddeJtU .i.n 1978, whLe.e. Ra.1..iJr. oad B had 50. It is necessary to know how "big" the railroads are. As another example, if a new segment of track is being constructed , it is impossible to pre dict how many accidents will occur on it, unless past ac cident rates are estimated and then extrapolated .
In the context of railroad accidents, several measures of industrial activity offer themselves :
1. Carloadings,
2. Train-miles ,
3. Car-miles ,
4. Ton-miles , and 5. Number of classifications in yards .
The choice mu st depend on reasonable evidence that accident numbers are , in fact, proportional to the chosen measure. In this sense, carloadings are an inappropriate measure. A car that is loaded and travels 1 mile to its destination certainly has a much lower probability of an accident than another that travels 1000 miles to its destination.
In the following paragraphs , the various alternative measures are discussed , and the mo st suitable ones chosen for the following groups of accidents :
• Mainline collisions ;
• Mainline derailments and all other types of accidents; and
• Yard accidents (derailments and collisions).
25 1. Ma inline Collisions
Approxima tely 75 head-on collisions occur on mainline track each year. To estimate how much this number might increase if the railroads were to suddenly increase the amount of freight they transport by a large amount , it is necessary to develop a theoretical model of what leads to a head-on collision . The model developed for this investi gation is described below.
Consider a single- track route segment that is L miles long , and carries traffic both eastbound and westbound . Trains traveling in opposite directions cross each other by the use of pass ing sidings. Once in a rare occasion , this does not happen as planned and a head on collision occurs . It is assumed that each "crossing" of trains is an event that is a potential candidate for a head-on collision. There
is a small probability, denoted by K, that any even t will lead to a head-on collision. If
E = number of events (crossings) per year ,
K = probability of a collision per ev ent, and
F = number of collisions per year ,
then the expected value of n is:
F = KE.
The value of E can be approximately determined as follows . Assume that there are N eastbound trains per year traveling at an average speed v mph, and a similar number westbound. The number of events experienced by any eastbound train can be computed as follows . From the moment it starts its trip to the moment it reaches its destination, a certain number of wes tbound trains will enter the route segment ; it must pass every one of them. It must also pass every westbound train that was en route at the. moment it started its trip.
26 Each eastbound train spends (L/v) hours en route. The number of westbound trains originating per hour is N/8760, where 8760 is the number of hours in a year. Thus , the number of new westbound trains that enter the segment is :
(L/v) (N/8760) trains.
The average time between westbound trains is (8760/N) hours . Their av erage spacing or headway is :
v(8760/N) miles .
On the average, therefore, the number of westbound trains that are on the segment at any given moment is :
(L/v) (N/8760) trains .
Thus, the number of encounters per eastbound train is :
2LN/876Ov .
Since there are N eastbound trains per year, the total number of encounters per year is :
(3-1)
and the number of head-on collisions per year will be proportional to this number.
If each train weighs G gross tons , the annual traffic density is :
2 D = �G tons per year .
This leads to an expression for N:
N = D/2G .
Equation (3-1) may now be re\rritten in the form:
If one now groups those route segments which have similar values for G and v, then these two factors can be treated as constants within
27 that group , and one has, within a group of track segments:
=
2 where 'j ' denotes the various groups, and = 1/(2 8760G Cj x vj ). Within a group , there will be several segments with parameters (L , D ) and so on . The total exposure within the group is : 1 l
= = (3-2) where i denotes each individual link.
Within a group, the expected number of accidents per year is :
= = which may be rewritten in the form:
(3-3) with being a group-constant, equal to �j Kj Cj •
Th e groups used in this report are the track classes . If one obtains historical data for:
The annual number of mainline head-on collisions • within each track class; and
The values of L and D for all mainline segments • i . within each track clas§ ; then Equation (3-3) can be· solved to obtain the constants ctJj :
/ = F. Lj . Dj / (3-4) J ri l.
28 One can now predict the a� pected number of head-on collisions on any segment , if one has :
• Its track class, j;
• Its length , L; and o. • Its traffic density , For then :
2 F = ¢ L 0 • (3- 5) segment j
Thus, accident frequencies (number of accidents per year) will 2 vary with a measure that can only be written as (ton) -miles. On segments of the same track class and of equal length, the accident frequency will vary with the square of the traffic density_ There is no simpler measure of accident rate that is useful for head-on collisions .
Similar considerations apply to other types of collisions , including :
• Rear end ,
• Side,
• Raking, and
• Broken-train, since they also depend on "encounters" between trains. Each will show an approximate proportionality between the number of accidents per year on a segment and the square of the traffic density on that segment.
It is therefore proposed that all types of mainline collisions be grouped together , sorted according to track class , and analyzed using Equation (3-4) . Predictions can then be made using Equation (3-5) .
29 2. Mainline Derailments
There are three possible candidates for exposure measures for mainline derailments: train-miles , car-miles , and ton-miles . Tradi tionally train-miles is used , but it was eliminated from consideration in this study because of its obvious shortcomings , including the strong likelihood [1] that , per mile of travel, a longer and heavier train has a higher probability of suffering an accident than a shorter one . The reasons are clear:
• Coupler failures become more likely as draft forces increase;
• Equipment defects become more likely as the number of cars in the train increases ; and
• Derailments caused by train action or collisions caused by an excessive stopping distance increase in probability as trains become longer and heavier .
A recent study [2] included a thorough evaluation of the two remaining alternatives : car-miles and ton-miles . It was concluded that each had desirable characteristics , and that neither was evidently preferable. Therefore both will be used in this report .
In summary , mainline derailment frequencies for a segment (numbers per year) are expected to vary with the length of the segment, and with either the number of cars (empty and loaded) traversing it per year or the gross tonnage of all traffic traversing it per year .
3. Yard Accidents
The only measure of yard activity that is readily available is the number of cars classified per year. Therefore, this measure is used in this report for yard accidents whether derailments or collisions . For each car traversing a yard , there is a certain probability of an accident . This probability is derived separately for collisions and for derailments.
30 D. HISTORICAL ACCIDENT STATISTICS
Accident data maintained by the FRA and by the MTB were analyzed to obtain a quantitative understanding of how many accidents occur annually , of what types, on what classes of track, on what types of track, due to what causes, involving what kinds of hazardous materials , and with what consequences . A representative selection of these analyses is presented here.
Accidents classified according to accident type, track class , and track type are enumerated in Tables 3-1 through 3-6, each of which is for one track class. The following important observations may be , made from these tabulations :
• Mainline and yard accidents account for 92% of all accidents;
• Derailments account for 73% of all accidents, while collisions of all kinds account for another 20% ;
• Accidents on Class 1 track account for 51% of all accidents; of these, almost 70% occur in yards ; and
• Some 73% of all collisions occur in yards, in contrast to only 36% of all derailments .
t�en the data are regrouped according to the choice of accident types and track types made in Section B, one obtains Table 3-7 , wh ich summarizes accident data. An important observation here is the sparseness of the accident data for Class 6 track. Statistical tests revealed that accident rates determined from these data would have a large standard error. Moreover , experience has shown that Class 6 track is not , by and large, a maj or cause of concern for safety . For these reasons , Classes 5 and 6 track are combined in all subsequent analyses.
Next , mainline accidents were grouped according to their causes .
The results are presented in Table 3-8. On the basis of the data presented in Table 3-8, it was concluded that track-caused collisions can be ignored ; therefore, accident rates are not estimated for them.
31 'fABLE 3-1. ACCIDENTS ON Cl.AS S TRACK 1 (1975-1977)
Na lu YHrd Sldjng In\hm try
Accjd�nt 'l'y lle • J.'rac . l� t:ac No . !t" rae. N . • No • No. o 1·'rSI!
Derai lment . 892 2489 .618 6558 .779 682 .689 608
(;ol Usion .013 Ilead-on 36 .016 174 .019 17 .022 19
1.1&1011 .021 Rear-end CoJ 58 .041 432 .062 54 .034 30
.031 87 .242 2568 .071 62 Side eu lUsion . 142 125
Rak ing Collision .007 19 .038 408 .018 16 .028 25
ColU.s lol1 .002 Brukt!ll '!' I'u in 6 .005 49 .005 4 .008 7 W N ltllilway 1I1ghway Crossing .014 40 .002 18 .002 2 .008 7
Crossing 0 '" 0 - - - - Grade. "II ,I 3
Obstruc tion .003 7 . 002 26 .001 1 .013 11
l!x(llos iou Ul! tonatlon - - 7 / .001 .001 1 .001 1 .007 18 .015 163 FJ Te:: /RuplUU! .022 19 .026 23
OtheT .010 29 .020 208 .019 17 .031 27
'rOTAI. 1.00 2790 1.00 10614 .999 875 1.002 883
Sou rce: Jt' RA RATltS TABLE 3-2. ACCIDENTS ON CLASS 2 TRACK (1975-1977)
Nu in ry YiJ cd Sid ing Iudu::>t:
Accident 'l'y p� .I!' rac. No. lO' ru(! • No. No. No • Frac . Frac.
De railment .878 3252 .607 928 .754 156 • 748 86
"ead-on Co11Jsion .013 47 .012 19 .010 2 .043 5
.020 73 .060 91 .073 15 .052 6 [(ear-end Co 11isJon
Side Co lli.s ion .016 58 .226 346 .073 15 .087 10
Collision .007 25 .043 66 .029 6 .026 3 Raking
Trajn Collis1'"1 .006 22 .005 8 .010 2 - - w Broken w lta ilway IUghway Crossing .037 138 .001 1 - - - -
Grad e Crossing .001 2 .001 1 .001 1 - -
Obs truc tJon .003 11 .001 1 - - - -
Expios ion/Ue tonat ion .001 2 .001 1 - - - -
l�t re /Rupttlre .008 29 .009 13 .015 3 .009 1
Othtn' .012 44 .035 54 .034 7 .035 4
1.002 3703 1.001 1529 .999 207 1.00 115 'l'O'l'AI.
Source: FRA RAI l{S TAB LE 3-3. ACCIDENTS ON CLA S 3 TRACK (1975-1977) S
Ma in i n Industry Van) S dI g
Accident Type r c. • No. l·'rac . No. Frac •. • 1!' a No. J.'ru(� No
Derailment .811 4038 .633 176 .731 76 • 84 6 11
Col lision .013 67 .022 6 .019 2 Head-on - -
l�ear-end Collision .030 147 .083 23 .067 7 - -
Side Collis ion .014 69 .191 53 .106 11 - - - Collis ion .009 44 .029 8 .039 4 - Raklalg Broken T n .008 42 .014 4 .029 3 .154 2 ra i ColIis ion I,..l � Crossing .057 284 .004 1 - Railway Highway - - -
Crossing '" 0 1 - - -- Grade - - .006 28 .007 2 Obs truction - - - - - Exp1os ion/Oetonat ion .002 8 - - - - -
Fi re/ltupturt: .020 98 .011 3 .010 1 - -
t .030 151 .007 2 - - - - O he r
1. 00 4977 1.001 278 1. 001 104 1.00 13 'l'OTAI.
------�: ou r ..:(!: FHA RAI RS 3-4 . 4 (1975-1977) TABLE ACCIDENTS ON CLAS S TRACK
MaIn Yart.! Siding Indu� try Accidtmt 'fy lle Frac . No. l" rae. No . {.'rae . No. Flac. Nu .
Dcrailtnent .693 2015 .649 96 .800 39 .667 10
Head-on Co11i�ion .021 60 ------
Colli.s ion 104 - - Kear-end .036 .020 3 .133 2
Side Co llision .022 64 .270 40 .143 7 .067 1
Raking ColUsion .019 55 .020 3 .020 1 - -
Broken 'l' ra in Colli�i()n .017 48 .014 2 - - - - W \.Il Railuay .091 264 - - - - .067 1 nigl,,�ay Cross ing
Grade Gro ssing .001 4 ------
nhs true t ion .006 16 ------
Explosion/DetonatJon "'0 1 ------
Vi /l .050 144 .014 2 .020 1 - - Other. 1.001 2907 1.001 148 1.003 49 1.001 15 TOTAL Source: FilA HAIR::; TABLE 3-5 . ACCIDENTS ON CLAS S 5 TRACK (1975-l977) Ha iu Yard Siding Illdu� try Acd dcnt Type I Frac . • No. Frul! . No . l� ruc No. L·'rac . No . I : Derai lment .718 442 .784 40 .750 12 1 .00 3 Head-on Col lision .020 12 ------ - Rear end Collis i.on .070 43 - - .125 2 - - Side Collision .016 10 .137 7 - - - - , Raking Co llision .034 21 .078 4 - - - - I Broken rra in Col lision .016 10 - - .125 2 - - W ' 0\ - - Railway Highway Crossing .057 35 - - - - -- -- - Grade Crostt ing - - - - - Obtt truction .007 4 - - - - - - Explos ion/De tona tion ------ "ir�/Rt1pturc .042 26 ------ Other .021 13 ------ 1' OTAI. 1.001 616 .999 51 1.00 16 1.00 3 Source: }lRA RAIRS - . ------�- .------. --- TABLE 3-6. ACCIDENTS CLASS TRACK (1975-1977) ON 6 Ma iu Yard Siding Indus tr.y Accident Type J.t' ruc. No. • No . Frac . No . I�rnc l,'rac. No . Derai lment .744 29 .800 8 - - - - Collision .026 1 ------Head-oll itt!ar-clld Collision ------ - - - - Side Co llision .026 1 .200 2 ------RakIng Col lts lon .026 1 Collis !(»l ------w Broken Train ...... ------kaihluy Highway Crossing .051 2 ------Grad,! Cross ing .026 1 ------Oba truction ------ExplosJon/Detollation Fi re/Uupture .026 1 ------ ------OLher .007 3 1.002 39 1.00 10 - - - - 1'O'fAl. " ------ Source; FRA RAIl TRACK l'YPI� MAINLINE YARD Track Class Collision s De railments Co llis ions Dera ilments 1 206 2,489 3,631 (,558 2 225 3,252 530 928 3 369 4,038 94 176 w co 4 331 2,015 48 96 5 96 442 11 40 6 3 29 2 8 Unknown 45 37 999 1,489 TOTAL 1,275 12 ,302 5,315 9,295 Sou rce : FRA/RAIR S TABLE 3-8. MAINLINE ACCIDENT CAUSES (1975-1977) ACCIOENT TYPE OERAIl.MENTS COLLISIONS Track Class Track-Caused Other Causes Track Caused Other Causes 1 1,548 941 6 200 2 1,628 1,624 7 218 3 1,507 2,531 11 358 I I , 4 639 1,376 11 320 I W \0 I 5 and 6 45 426 3· 96 Unknown - 37 - 45 I I TOTALS 5,367 6,935 38 1,237 Source: FRA/RAIRS Investigations were made of the frequency with which hazardous material releases occur in rail transportation; these data are shown in Table 3-9, as a function of the amount of property damage caused by the hazardous material . Two facts are ev id ent from this tabulation: 1 . A large majority of hazardous-material releases are not of major consequence; in fact, 76% cause property damage of less than $100 per incident ; and 2. Among the more severe incidents, the vast maj ority (31 out of 38, or 82%) are caused by just three chemical groups : flammable gases , flammable liquids, and corrosives. These conclusions are bolstered by the data shown in Figure 3-1, for the number of injuries attributable to each chemical group over the years from 1971 through 1977 . E. HISTORICAL DATA ON EXPOSURE 1 . Mainline Operations The data shown in Table 3-10 were provided by the Transportation Systems Center . The data are based on estimated flows on the FRA Network Model , developed by using a routing algorithm and data from the FRA 1% waybill sample for 1976, along with statistical techniques for scaling up the waybill sample. It is useful to know how to relate train-miles , car-miles, and ton-miles with one another. First however , it is necessary to know the relationship between: • Empty and loaded car-miles; and Revenue and ross ton-miles. • g In 1976 , 55.5% of all car-miles were generated by cars carrying cargo ; the remaining car-miles were generated by empty cars being returned to a point wh ere they could pick up another load [3 ]. Car-mile data 40 TABLE 3-9 . COMPARISON OF DOLLAR DA MAGE* RANGES FOR IIAZARDOUS-l-tATERIAL COMMOUITY GROUPS No. l<' ract ion with dollar damage of Greater Releasing 500- 1,000 than (1971-1977) 0 0-1 1-10 10-30 50-100 100-500 500,000 2,000 2,000 Explosives 42 0.29 0.36 0.05 0. 10 0. 14 0.05 0.02 0.02 0.02 Non-flammable Gas 378 0.50 0.43 0.05 0.02 Flammable Gas 562 0.45 0.42 0.04 0.04 0.02 0.02 1\,0 "'0 "'0 Flammable Liquid 1043 0. 31 0.54 0.09 0.06 0.01 0.01 Flammable Solid 86 0.33 0.54 0.11 0.02 "'0 Oxidizer 325 0 . 10 0.80 0.08 0.03 Organic Peroxide 1 1.00 � Toxic 190 0.21 0.63 0.10 0.05 0.01 0.01 � I Radioactive 6 0.50 0.33 0.17 Corrosive 1749 0.41 0.51 0.06 0.02 ",0 ",0 TOTAL 4382 * Includes damage due to the hazardous ma terjal only . Source: MTB . Source: MTB FIGURE INJURIES BY COMMODITY GROUP 3-1. BASED ON RELEASES. 1971-1977 42 'fABLE 3-1 0. MAINLINE EXPOSURE I)ATA t-leasure of Exposure Class of Track i 3 4 5 6 AU. 1- 2 & 6 Loaded car-Miles (10 ) 145.1 585.3 2,237 10,650 1,745 15 , 360 6 i Total Ca r-Miles (10 ) 261.2 1,055 4,031 19,180 3,144 27,680 (a) 2 12 Total Car-Miles (10 ) 147 388 1,050 8,390 2,180 12,100 9 Revenue Ton�Mil es (10 ) 7.56 30 .5 117 555 90.9 800 .p I.\) � 15 Revenue Ton Miles (10 ) 123 324 878 7,010 1,820 10,100 9 Gross ·fon-Miles (10 ) 15.6 62.8 241 1,140 187 1,650 2 15 Gross Ton-Miles (10 ) 520 1,370 3,710 29, 700 7,700 42, 700 ------ Source : TSC and Arthur Little, Inc. , estima tes . D. Assumptions : 52 .1 Revenue Ton-Miles per Loaded Car-Mile _ 0.555 Loaded Car-Miles per Total Car-Mile • 30 Tons Ta re Weight per Car • (a) Computed as follows : for a segment , mUltiply length (miles) by the square of the number of cars traversing the seg ment ; take the sum overall segments in a given track class . developed from an analysis of the 1% FRA waybill sample include only loaded car-miles , since waybills are not required for empty cars . These data mu st be multiplied by the factor (1/0.555) to obtain total car-miles. Similarly, ton-miles obtained from the waybill sample are revenue ton-miles ; i.e. , the tonnage of the freight multiplied by the distance it travels . What is required, however , is an estimate of gross ton miles. To obtain this value, one assumes the average tare (empty) weight of freight cars to be 30 tons. �is weight is transported by every car for every mile it travels, whether loaded or empty . Therefore , the "dead" ton-miles are: - (loaded car miles) x (30/0.555) . When this number is added to the revenue ton-miles , one obtains an estimate of gross ton-miles . . 2 . To 0 b ta�n t h e gross-ton -m�1 es est ima tes, one h as to square th e ratio of gross ton-miles to revenue ton-miles and mUltiply it by the 2 net ton -ml..1 es . If one wishes to perform a risk analysis of either a specific train or a "typical" train , one has to know how may cars are in it (N )' or what its gross tonnage is (G) . Then, per train-mile , one has T N car-miles and G gross ton-miles . For the typical U.S. train, T N 67 cars (3] , and G is estimated to be about 4500 tons . However , T = N can vary from a theoretical lower limit of 1 to a practical upper T limit of about 200. Gross tonnages may vary from a low of a few 100 tons to a maximum of perhaps 15 ,000 tons. Some of the exposure data shown in Table 3-10 may be compared with data published by the AAR [3] and the Interstate Commerce Commission [4] . For example, the total car-miles shown in Table 3-10 9 for all track classes is 27.7 x 10 • For 1976, the comparable AAR 9 number is 28 .5 x 10 • The revenue ton-miles shown in Table 3-10 add 9 9 up to 801 x 10 • The comparable &� R number is 791 x 10 ; the ICC figure 44 9 (for Class I and Class II railroads) is 800xlO . Th e agreement between the various sources is satisfactory. Neither the AAR nor the 2 ICC cites gross ton-mile figures. In addition , the ton -mile measure is apparently being used for the first time. Estimates do not appear in any source outside of this report . Despite the good agreement on the totals , the exposure data by track class may contain inaccuracies due to an assumption; viz., that the ratio of revenue ton-miles to loaded car-miles as well as the ratio of loaded car-miles to total car miles , is independent of track class. Since data on the variation of these parame ters with track class are not available, the track class exposure data in Table 3-10 represent the best estimates possible at present. 2. Yard Operations A recent FRA study [5] provides estimates of the number of cars classified each year in yards of all types. Although it is clear that yard classification risk will vary, depending on whether one is examining flat or hump yards, this variable was excluded since informa tion concerning it is not available on the FRA Network M9del , which is to be the basis for future risk analyses . The total number of cars classified per year in all classification yards in the U.S. is 8 approximately 3.9xlO • F. HISTORICAL ACCIDENT RATES Data on historical accident frequencies (numbers per year) are presented in Section D. The appropriate measures of exposure for defining accident rates are presented in Section C. Historical data on exposure are presented in Section E. This section combines information from all three of these sections to develop estimates of historical accident rates . 1. Mainline Derailments When the numbers in Tab le 3-8 are comb ined with the numbers in Table 3-10, one obtains the mainline derailment rat es shown in Table 3-11 . (Note that Table 3-8 contains three years' data, whereas 45 TABLE 3-11. HISTORICAL MAINLINE DE RAILMENT RATES Class of Track 2 4 5 and ALL * 1 3 6 I Derailment Rate--All Causes 53.2 17.3 5.59 0.589 0.840 2.49 . 9 ( Accidents per 10 Gross Ton-Miles) Derailment Rate of Track- 33.1 8.64 2.08 0.187 0.080 1.08 Caused Accidents 9 (Accidents per 10 Gross � Q\ Ton-Miles) Source: Arthur D. Little, Inc. * Includes accidents with WlknOwn Track Class. i: j Table 3-10 contains estimates of only one year 's exposure. For the two to be on the same basis , the numb ers in Tab le 3-8 must be divided by 3.) The quirk that is observed in Table 3-11 in the rate for Class 5 & 6 track (which is higher than that for Class 4 track) is probably anomalous , although no specific source of error has been found so far. Th e po ssible errors arising from any anomalies are not large , however, since Classes 5 and 6 track account for only 8% of all gross ton-miles , as can be seen from Tab le 3-10, and for only 4% of all accidents, as can be seen from Table 3-8 . 2. Mainline Collisions As for mai nline derailments , the data in Tables 3-8 and 3-10 can be appropriately comb ined to obtain ra tes for mainline collisions . These are shown in Table 3-12. Rates are not estimated separately for track-caused collisions since they are low, as can be seen from Tab le 3-8 . 3. Yard Accidents Yard accident frequencies (three years' data) are provided in 8 Table 3-7. In Section E, it was estimated that approximately 3.9x10 cars are classified each year. One can thus ob tain the following estimates of yard accident rates : Yard collisions 4.5 per million classifications ; and Yard derailment s 7.9 per million classif ications . G. TRAIN ACCIDENT FREQUENCIES AND PROBABILITIES It is important to make a distinction between the ac cident rates estimated in Section F a nd accident frequencies and probab ilities. Suppose one is analyzing a situation in which the exposure per year (gross ton-miles per year, for example) is E, and the accident rat e is Z (accidents per gross ton-mile, for example) . Then the expected frequency of accidents annually is : 47 TABLE 3-1 2. HISTORICAL MAINLINE COLL ISION RATES Class of Track 1 2 3 4 5 and 6 ALL* .c: Collision Rates--A11 Causes 13.2 5.47 3.32 0.372 0.429 0.990 oo 17 [Accidents per 10 (Gross Ton)2-Mi1esl ------Source: Arthur 1>. Little, Inc ., est imates . * Includes accidents with unknown Track Class . " \. \ . " = E Z. (3-6) If it is assumed that accidents occur as a Poisson process, then the probability that there will be precisely F accidents in a year is : F -m F p(F) = (�) e (3-7) Ft The probability that there will be at least one accident is "the probability of an accident ," P : A = p(F 1) 1 p O 1 - e - (3-8) P � = - ( ) = � A When m is small, m and pel) ; then m is large, approaches P = F P : F P unity. A A A The same argument can be extended to examine the frequency of accidents to trains carrying hazardous materials . Let P represent the H probability that a train involved in an accident is carrying hazardous materials . Then the expected frequency of accidents to hazardous material trains is : (3-9) Furthermore, the probability that at least one hazardous-material train will suffer at least one accident is : P 1 e = (3-10) AR - -� If P is= small, then P P ' H : H � AR � The expected frequency of accidents can be shown as a function of the probability of an accident: 1 2n( . (3-11) 1 _ P A ) 49 Thus , the frequency of hazardous-material accidents is : = (3-12) One pertinent observation that may be made is that when the expected frequency (number of accidents in a year) is small, then the probability of an accident (per year) is numerically equal to the frequency. When the expected frequency increases, however, the proba bility tends asymptotically to a value of unity. This difference is relevant to analyses of risk in situations where multiple accidents are expected to occur. H. REFERENCES 1. Leilich, R. H. , "Study of the Economics of Short Trains , Prepared by Peat, Harwick, Hitchell and Co ., NTIS Report No . PB-235II -4ll, June 1974. 2. Nayak, P. R. and Palmer , D. W., "Issues and Dimensions of Freight Car Size: A Compendium," Report No . FRA-ORD-79/56 , March 1980. 3. Association of American Railroads, "Yearbook of Railroad Facts ," 1977 Edition. 4. "Transport Statistics in the United States, Year Ended December 31 , 1976" (Part I: Railroads, Their Lessors and Proprietary Companies), Interstate Commerce Commission. 5. Petracek, S. J. , et aI , "Railroad Classification Yard Technology ," Report No . FRA/ORD-76/304 , January 1977. 50 4. NUMBER OF CARS DERAILING A. INTRODUCTION One of the inputs required by the model presented in Chapter 2 is the probability distribution of the number of cars that derail or are damaged in a typical accident. It is assumed not �n1y that this number is a random variable, but also that the number is strongly dependent on train speed and not on train length. The latter assumption is more or less justified for trains that are more than 25 cars long , as may be seen from the data in Appendix B. The following paragraphs provide historical data on the number of cars derailed or damaged , along with best-fit estimates of the mean and variance of this random variable, as functions of speed . B. YARD AND MAINLINE DERAILMENTS--ALL CAUSES Federal Railroad Administration accident data were analyzed to (FRA) obtain the values of means and standard deviations for N (the number D of cars that derail in an accident) displayed in Table 4-1. Upon examining the data, three issues of concern become apparent. The first is the dip in av erage derailment sizes in the 55- to 60- mph range. From a statistical viewpoint , the t-statistic based on the difference in average derailment size between 56- to 60 - mph derailments and 31- to 55- mph derailments (for yard and mainline combined) is : 8.40 - 11 .8 - 2.8. 10.0 + 11.13 = 130 2105 I I On the basis of these two nu mbers alone, the drop is significant at the 1 percent level, but the drop could be statistical. On examin ing the data, the difference appears to be due mainly to the low 51 TABLE 4-1. MEANS Al�D STANDARD VARIATIONS OF THE NUMBER OF CARS DERAILING (DERAIL.'1ENTS DUE TO ALL CAUSES) MAINLINE YARD I Da a a Da a a � N t � N Speed t D D D D Points Points 0-5 1643 4.80 4.30 7263 4.21 3.78 5-10 3177 5.51 4. 72 1765 4.75 3.04 11-15 1193 5. 69 5.04 187 4.83 3.61 16-20 1398 6.35 5.48 40 5.22 3.65 21-25 1546 7.74 6.94 12 7.58 3.99 26-30 1056 9.65 8.54 8 7.13 7.43 31-35 522 11.30 9.86 6 12 .17 10.98 36-40 662 11 .36 11.07 5 6.0 2.74 41-45 343 11.05 11 .16 5 5.0 4.06 46-50 387 11. 04 12.45 1 27.0 0.0 51-55 169 10.93 12 .17 - -- 56-60 128 8.13 10 .09 2 2.5 2.12 61-65 37 14.49 15 .68 - - - 66-70 38 12.42 12. 37 - - - 71-75 1 4.0 - - - - 76-80 - - - 1 4.0 0.0 >80 1 2.0 - - -- 52 incidence of derailments of more than 30 cars for 55- to 60-mph derailments (5 out of 128 compared with the 49 out of 557 incidents for derailments in the 45- to 55-mph range) . The significance of this difference is about 7 percent . One might have expected 11 derailments with fewer than 30 cars derailing in the 55- to-60-mph range, and this might have increased the mean value to 10 or 11. Consequently, a statistical explanation is not completely unreasonable. The second issue is the possible existence of bias in the esti mation of speeds . Figure 4-1 presents' a comparison of statistics for those derailments* in which the speed was recorded and those for which the speed was estimated . None of the differences is extremely signifi cant , the ma�imum t-va1ue being 2.12. However , the aggregated differ ence over all speed classes , which is equal to the sum of t-va1ues divided by the square root of the number of speed classes , is 3.05. Although this does not alter the estimated curve a great deal, it should be noted that there is an effect that may be caused by biasing toward lower values in the estimation of speeds. This difference may also explain the dip in derailment lengths in the 55- to-60-mph range. (Many of the large derailment accidents may have been recorded at different speeds .) Because recorded speed data are limited and the magnitudes of differenc es in Figure 4-1 are not large, both recorded and estimated speeds were used in subsequent analyses . The final issue is the comparison of means and variances for yard and mainline derailment in each speed range. The statistical tests of significance are presented in Table 4-2 . As shown in this table, there are statistical differences, especially at low speed values , for which there are a great deal of data. However , the development of separate best-fit curves for yard and mainline accidents is unnecessary * For some derai1ments, the appropriate data field was blank , and it was not known whether the speed was recorded or estimated . These are omitted . 53 15 Mainline Derailments 14 Recorded Speed 13 12 __ ....:Estimated and � Recorded Speed 11 en 10 .5 .;... QJ 9 c VI ... ftI U 8 - 0 ... QJ .c 1 E ::I Z c: ftI QJ � 4 3 2 0.10 11-20 21-30 31-40 41-50 51-60 61-70 11-80 81-90 Speed Range FIGURE 4-1. NUMBER OF CARS DERAILING: COMPARISON OF RECORDED AND ESTIMATED SPEED 54 'fABLE 4-2 . SIGN IFICANCE TESTS FOR DIFFERENCES IN THE MEANS AND VARIANCES OF NUMBER OF CARS DE RAILING AT VARIOUS SPEEDS FOR MAINLINEAND YARDS t-valuc for Difference in I value for t. Speed Means S ignif icance Two Variances Significance -4 0-5 3.92 10 1.29 Zero -7 6-10 4.86 10 2.4 Zero i 11-15 2.09 4% 1.95 Zero 16-20 1.56 12% 2.25 "'0. 4% I 21-25 .12 Not: sign ificant: 3.0 "-4% 26-30 .87 Not: significant 1.32 Not: significant VI VI 31-35 . 18 Not: significant .8 Not: significant 36-40 3.23 ",1. 5% - 16 .3 ",2% 41-45 2.5 ",5% 7.5 ",15% 45-50 1. 28 "'20% - - 56-60 .7 Not: sign ificant - - -- because the differences are ,not large in magnitude, even though they are statistically significant: speed explains most of the variance in the number of cars derailing . For this reason, curves were fitted to the combined data. The mean value of N is denoted by UL. (v) and its variance by 2 (1 (v) . A comprehensiveo regression analysNOis was made to determine a No . simple curve that best fit the data. Both weighted regression and unweighted regressions were used to de termine the best fit. Table 4-3 displays the results of the analysis . The statistic is given by: r* n * ... 2 F [f(v) - f(v) ] (4-1) = i l W' where 1 f(v) = empirical function , f(v) = estimated function, fO; unweighted scheme, = nN 'L N for weighted scheme , which allows for a 11 i i direct comparison of the schemes . I Based on Table 4-3 , the following functional forms are utilized : O 5 = 1. 7v • � Mainline and Yard Derailments 2 O (4-2) = (1 2 . 7v • (All Causes) N I O The raw data as well as these regressions are shown in Figure 4-2. For the best one-parameter fit is nearly optimal for the ' unweighted� ofit and moderate for the weighted fit (although the percen tage of the variance explained in the latter case is still 78% and the percentage of the total sum of squares explained is 97 .3%) . The 56 TABLE 4-3. MEANS AND STANDARD DEVIATIONS OF THE NUMB ER OF CARS DERAILING (DERAILMENTS DUE TO ALL CAUSES) 2 "N �p 0 Welsh ted Fit .. nctlonol Unweishtcd Unwe hted Fit Weishted Fi �· Fit y .. t d c d F" c d F c Fo\Om C fit d F· 4.836 .1241 3.8786 .1654 6.396 5.395 2.869 1.120/. 2.6011 7 r. + .Iv lJ.98 11598 1 48 O 5 1.67/. l.lltl 28. 7ft 1.776 . 2 6.139 70.39 29. 56 1]309 -28.15 6 3630 c + ,lv . 1 3 3 19 . J 6.696 . 52 4.974 .00306 33 .71 .0376 15196 16.641 .0535 c + ell 001 5O.U 19.072 1918 VI c + d log v - .464 2.937 32.27 1.563 7 2. -105 61.15 19722 -27.419 29.688 64 27 ..... 2 . 12 1 83 .315 113 dv .2271 Ill .81 2. 754 11697 2.(,51 1757 O .5 dv 1.6074 32 .81 1. 7678 15.78 18. 394 20505 12 .5795 5902 .. .0378 }26 .JJ Not attempted .0481J9 Not at dv- 22191 t(!mptiHI d 2.65 .360 7.98 11833 cv 3.12 .322 311. 7 1.472 1. 162 6.11 .673 3200 dv 40.8 4.481 .02 12.03 .0325 16921 ce 6.0 .0115 23. 7 Not ottelDl,ted • nlc total variation (around the meau f') to which F can be compa red is: Unwcishted �e l.s!!..tcd a(v) 121 70 b(v) 58416 171ill 18 ri------� 15 • 150 A 12 A A ffi 2 N 100 /JN O • O 9 V' A 00 6 50 • A Historical Values of A ffiN o • Historical Values of 3 • uN o • 0 �,,�=------L------L------� ------� ------10 10 20 _L30 _:40� 50� 60;_ _;70 Spend (mph) FIGURE 4-2. HISTORICAL VALUES FOR m AND AND ESTIMATED FUNCTIONS N u tl�D one-parameter shape is far easier to use in further analyses , however, and was chosen for this reason . For the case of b(v) , the one-parameter fit is nearly optimal . C. YARD AND MAINLINE DERAILMENTS DUE TO TRACK CA USES Track-caused derailments are longer than the set of all derailments. The data are ,presented in Table 4-4 . Th e general functional forms are assumed to be the same, but with a different parameter value for a(v) only. The functional equations estimated to give the best fit are : = 2 • 1 v 0.5 , Track-caused Yard and Mainline Derailments (4-3 ) = 2.7v D. COLLISIONS The maj or differences between collisions and derailments are in the functions of �. and Table presents the aggregated N aN ' 4- D D 5 statistics for the number of cars derailed (or damaged) in those collisions for which at least one derailing car was reported . Based on these statistics, the following functional forms were determined to be the most appropriate for collisions . = •••• Yard and Mainline Collis ions (4-4) = 2.3v E. COLLISIONS WITHOUT DAMAGED CARS A relatively large number of collisions in which no cars are described as either derailing or being damaged have been recorded by the FRA. It is important, in the context of the model of Chapter 2, to determine what proportion of collisions fall into this category, and eliminate them from further conside ration. 59 TABLE 4-4 . MEANS AN'D STANDARD DEVIATIONS OF THE NUMBER OF CARS DERAILING (TRACK-CAUSED DERAILMENTS) Mainline Yard Speed Data a Data a � N � N (mph) Points D D Points D D 0-10 2875 5.624 4.737 5322 4.447 3.244 11-20 1153 6.867 5.131 100 4.960 3. 124 21-30 1162 10 .219 7.626 8 7.5 5.1 31-40 368 15. 554 11.074 2 5.0 - 41-50 128 17. 867 12. 704 4 9.75 10.305 51-60 43 16 .674 11. 767 - - - 61-70 6 15 .333 12.867 - - - 71-80 - - - 1 4 - 60 In the following , it is assumed that P is the fraction of CD collisions in which at least one car is damaged or derailed . The specific number of interest is contained in Table 4-5: 0.54. PC = We thus have the following result for yard and mainline collisioD ns : ' ' = 0.54 (fraction of collisions in which at least one car is derailed or damaged) , - P = 0.46 (fraction of collisions in which no 1 CD ' cars are derailed or damaged) . 61 TABLE 4-5. STATISTICS FOR THENUMB ER OF CARS DERAILED OR DAMAGED IN COLLISIONS Speed Number P oN CD (mph) of Points �D D 0-5 3223 2.1 2.0 .56 6-10 383 2.7 2.3 .53 11-15 100 3. 7 3.8 .46 16-20 53 4.7 8.0 .52 21-25 39 5.3 6.5 .57 26-40 32 6. 8 6.3 .47 31-35 13 9.4 9.0 .35 36-40 26 8.0 9.0 .43 41-45 14 7.1 5.3 .47 46-50 11 15.1 14.3 .48 51-55 4 '* '* '* 56-60 7 'if '* * 61-65 1 * 'if * 66-70 1 'if * '* 71-75 1 * * * 76-80 1 'if * * >80 1 * * * Overall 3910 2.5 3.0 .54 i: Insufficient data. 62 5. PRESENCE OF HAZARDOUS-MATERIAL CARS IN TRAINS A. INTRODUCTION An input needed for the model presented in Chapter 2 is the probability that a train suffering an accident carries hazardous may be assigned a value material cars. This probability, denoted by PH, of unity if one is examining the risk associated with trains known to be carrying hazardous materials. On the other hand , if one is analyzing more aggregated risks , historically based estimates of P are useful. H These estimates are presented in this chapter. The value of P for a given large collection of traffic is deter H mined by another characteristic parameter , the ratio of hazardous material cars to all cars . This parameter is denoted by w o Its H historically observed values are presented . The relationship between P and is explored , and formulas are presented for estimating P H �H H values from given values of � ' H B. RATE OF OCCURRENCE OF HAZARDOUS-MATERIAL CARS The proportion of hazardous-material cars to all cars in a typical train is denoted by 0 ' Thus , if: H N hazardous-material cars per train, and H = N total number of cars per train , T = then ( 5-1) One estimate of � can be obtained by dividing the loaded car-mile H estimates for hazardous materials with those for all commodities (data provided by TSC) : 8 4.4 x 10 � = 0.029. . H = 10 1.5 x 10 63 An alternative es timate of � can be obtained by assuming that H a hazardous-material car has the same probability of being involved in an accident (i.e. , being derailed or damaged) as any other car . Then : (5-2) where = number of hazardous-material cars derailed or damaged , and � total number of cars derailed or damaged . Data regarding the value of � estimated in this fashion for H derailments are shown in Table 5-1 . For collisions , the historical values of n were found to be as H follows : = 0.020 for all mainline collisions ; and = 0.025 for all yard collisions. C. PROBABILITY THAT A RANDOM TRAIN CONTAINS HAZARDOUS-MATERIAL CARS Given an aggregation of traffic in which a fraction of rrH all cars cons ists of hazardous-ma terial cars , there will be a fraction P of all trains that contains one or more hazardous- material H cars. There is no direct observation available of this parameter . However , it may be approximated as follows : No . of Accidents to Trains Carrving HazardouS-Material Cars (5-3) Total No . of Accidents When one attempts to estimate P in this manner for the various comb H i nations of track type , accident type, track class , and accident cause, the data are found to be sparse , and the estimates are subj ect to large errors. A way to circumvent this difficulty is to estimate the rela tionship between P and train speed , aggregating over all other H 64 TABLE 5-1 . FRACTION OF DERAILING CARS THAT CONTAIN HAZARDOUS MATERIAL Location N N 7T M N HO O H = HO/ o Main 1635 89066 .018 Yard 706 41578 .017 Siding 117 5287 .022 Industry 84 3545 . 024 Other --12 615 .020 TOTAL 2554 140091 .018 Main--Class 1 190 13883 .0137 Main--C1ass 2 400 21396 .0187 Main--C1ass 3 670 31873 .0210 !1ain--C1ass 4 280 16560 .0169 Main-- Classes 5 & 6 54 3754 0.0144 65 factors . An approximate value of P is then obtained for each subset H of accidents by estimating the average train speed for that subset and obtaining the corresponding value of P . H The histor ical relationship between P and train speed is shown H in Table 5-2. The derived values of P for various accident subsets H are shown in Table 5-3 . D. EXTRAPOLATION OF " and P VALUES H H The values of P are based on an underlying grand average value of H H which can be seen from Table 5-1 to be 0.018 . If this value were H ' to change--due to a change in the level of hazardous material being transported--both the rr values in Table 5-1 and the P values in H H Table 5-3 would change as well . A reasonable assumption for the values for the accident nH subsets is that they would all change in the same proportion as the grand average Thus, if the " value for all traffic doubled from nH• H 0.018 to 0.036, one might expect for mainline Class 1 accidents to "H double from 0.0137 to 0.0274. The change in P values is somewhat more complex . Consider a H train with N cars . Assume that hazardous-material cars occur in groups T or blocks , the size of the block being G • The train has (N /G ) blocks , H T H each of which might be a hazardous-material block with probability " ' H The probability that none of the blocks is a hazardous-material block is also the probability that the train carries no hazardous material cars, and is given by: 1 - P = = H exp (5-4) :: exp 66 TABLE 5-2. RELATIONSHIP BETWEEN P TRAIN SPEED H AND Speed P H (mph) 0-5 .058 6-10 .066 11-15 .076 16-20 .103 21-25 .108 26-30 .135 * > 31 .150 Average . 08 *Aggrega ted because of limited data. 67 TABLE 5- 3. ESTIMATED PROBABILITY THAT A TRAIN IN &� ACCIDENT IS CARRYING HAZARDOUS MATERIALS Accident Group Probability P H Yard derailments .057 Mainline derailments .097 Hainline Class 1 derailments .052 !-fainline Class 2 derailments .091 Mainline Class 3 derailments .123 Mainline Class 4 derailments .114 Ma inline C1aSS2S 5 and 6 derailments .128 Track-caused yard derailments .063 Track-caused mainline derailments .086 Yard collisions , N > 0 D .081 Ma inline collisions , � 0 O > .090 Hainline Class 1 collisions , N > 0 .071 D Hainline Class 2 collisions , N > 0 .082 • 0 Ma inline Class 3 co llisions , N > 0 .095 0 Hainline Class 4 collisions , N 0 O > .101 :-!ain1ine Classes 5 and 6 collisions , N 0 O > .110 68 Thus: (5-5) Designate by P� and �� the values corresponding to a hypothetical scenario, and by the value corresponding to When PH �H = 0.018. Equation (5-5) is applied to these two pairs of values , the result can be combined to yield the follow ng extTapolating equation for i PH : 0.018 (5- pi = - ��) / 6) H 1 (1 - P H 69 6 . NUMBER OF HAZARDOUS-��TERIAL CARS DERAILING A. INTRODUCTION When an accident to a train occurs, a certain number (N ) of HD hazardous-material cars derail . This number is a random variable, (�1) strongly influenced by the total number of cars derailing , N , and the D proport ion of hazardous-materials car to all cars ' � . This chapter H presents an approach to estimating the probability distribution of N The approach is to estimate the mean and variance of N , and HD• HD then to fit a gamma distribution to these parameters. The continuous gamma distribution is then made discrete to obtain the distribution of N Formulas are presented for the mean and variance of N • The HD • HD gamma-fitting procedure is then described . This method is intended for use in situations in which the exact number of hazardous-material cars in a train is not specified . When the number is specified , a more complex model is necessary. This model is presented in Appendix B. The obj ectives of this work did no t call for its numerical application. B. GENERAL STATISTICAL FORMULAS Much of the analytical development presented in the following pages uses the two following expressions (1] : E(Y) E(E(y X» = (6-1) I and Var (Y) = E(Var (y X» + Var (E(y X» (6-2) I I 70 wh ere E() denotes mean or expected value, Var () denotes variance, and denotes tty given ylX X.II Both Y and are random variables . X C. MEAN AND VARIANCE OF NUMBER OF HAZARDOUS-MATERIAL CARS DERAILING Let N denote the total number of cars derailing or damaged in an O accident, with N denoting the number of those that carry hazardous HD materials. To compute the expectation and variance of N given N we assume HO O ' that cars are in blocks of length G , a random variable. If the over H all rate of occurrence of hazardous-material cars is � ' then the H expectation of N given N and G is : HO o H = (6-3) The number of blocks derailing is (N !G ). For any of these D H blocks, there is a probability � that it is a hazardous-material block H with G hazardous-material cars, and a probability (1 - ) that it is H �H not a hazardous-material block. The number of hazardous-material blocks can be taken to be a random variable with a binomial distribu tion with probability parameter � . The variance of the number of H hazardous material blocks , given (N !G ) total blocks derailing is D H therefore [2] : 71 Since each block contains G cars, the variance of the number R of hazardous-material cars derailing is: (6-4) Equation (6-2) is next applied to Equation (6-4) to remove the conditional dependence on G " The result is : R (6-5) where When Equation (6-2) is applied once mo re to Equation (6-5) , one : ob tains the unconditional variance for NRD (6-6) Similarly, the unconstrained mean value of NHO is obtained by combining Equations (6-1) and (6-3) : (6-7) In Chapter 4, it was determined that the following general expressions hold : E(N lv) 0.5 D - = d v (6-8) �D and 2 Var(N lv) :: ev, D - (J (6-9) ND where v is the speed . The values of d and e are shown in Table 6-1. 72 TABLE 6-1. VALUES OF REGRESSION CONSTANTS FOR MEANN A D VARIANCE OF ND Constant Accident Category d e Mainline and Yard Derailments 1.7 2.7 (All Causes) Mainline and Yard Derailments 2.1 2.7 (Track-caused) Mainline and Yard Collisions 1.25 2.3 (Given at least one derailing car) O.5 Note: E(N ) - dv D = �D 2 Var(ND) - a = ev N D 73 The unconditional means and variances for NO can be obtained by applying Equations (6-1) and (6-2) to (6-8) and (6-9) : (6-10) and (6-11) Var(NO) = e E(v) + d var(vO.S). The mean and variance of vO.S and the mean of v is to be taken over the accident subset that is of interest. When Equations (6-10) and (6-11) are made conditional on the variables rr , rc� AT and AC, and are then introduced into Equations (6-6) and (6-7) , the final, desired expressions are obtained: (6-12) E(NHOITT, TC, AT, AC) = �Rd E(vO,SITT, TC, AT, AC) . and Var(NHOITT,rc , AT, AC) (1 - � = n ) m d E(vO,SITT, rc, AT, AC) R R GR 2 + + O (6-13) 'K {(e d) E(vITT, TC, AT, AC) - d [E(V OS TT, TC, AT, AC] } In Equation (6-13) , the followingresult has been used: var(vO.5 TC, AT, AC) = E(vITT, TC, AT, AC) :'rT, 5 2 - [E(VO. ITT, TC, AT, AC] 74 Historical data are not available for the parameter mG . A value of m 4 was chosen on the basis that this provided the b st fit G = betwe n his torical values of the mean and variance of the numb� er of hazardous-m� aterial cars releasing their contents, which are analyzed in Chapter 8. O.5 Values of the conditional means of v and v are given in Table 6-2. These are obtained from FRA accident data. Note that for collisions, the mean values are only for those accidents in which at least one car was reported as being damaged or injured. Thus , when the values from Table 6-2 are used in Equations (6-12) and (6-13) for collisions, the resulting distribution of NHD is conditional on a collision having occurred which N 1.0. For a random collision , it D � was noted in Chapter 4 that the probability that N 1 is P 0.54 D � CD = . D. FITTING A DISTRIBUTION TO THE �� S AND VARIANCE Historical data on the number of hazardous-material cars derailing in accidents are shown in Table 6- 3. Several one- and two-parameter distributions were fitted to the se data, and the gamma distribution was found to approximate the data most accurately , using the Kolmogrov Smirnov test. The gamma distribution was , therefore, chosen as the generic form for curve-fitting purposes . When a distribution is developed using the means and variances given in Equations (6-12) and (6-13) , it is found that large inaccura cies can occur in the tail of the distribution, essentially because of the large probability that MHD = 0. This large probability exists because of the large probability (1 - P that a train in an accident H) contains no hazardous-material cars . A procedure was therefore developed which yields a gamma distribution conditional on hazardous material cars being present in the train. The conditional means and variances for N HD are : = (6-14) 75 6-2 . VALUES OF TABLE MEAN v AND vO.S Mean value of 0.5 Accident Group v v Yard derailments 1. 89 3.96 Mainline derailments 4.03 18. 9 �ain1ine Class 1 derailments 2.67 7.95 Mainline Class 2 derailments 3.68 14 .9 Mainline Class 3 derailments 4.38 21 .3 Mainline Class 4 derailments 5.17 29 .7 Mainline Class 5 and 6 derailments 5.81 37.6 Track-caused yard derailments 2.28 5.86 Track-caused mainline derailments 3.53 14 . 6 Yard collisions (NO > 0) 1. 74 3.29 �lainline collisions (NO > 0) 3 .06 12.6 > Ma inline Class 1 co llisions (ND 0) 2.15 5.57 Mainline Class 2 collisions (ND > 0) 2.73 9.09 Ma inline Class 3 collisions (NO > 0) 3.26 13.6 Mainline Class 4 collisions (No > 0) 3.51 16.5 Mainline Class 5 & 6 collisions (No > 0) 4.18 23.5 76 TABLE 6-3. NUMBER OF HAZARDOUS-MATERIAL CARS DERAILING OR DAMAGED PER ACCIDENT No . of Cars Derailing No . of Accidents 0 32,083 1 708 2 236 3 145 4 83 5 40 6 27 7 17 8 7 9 6 10 4 11-15 14 16-20 6 20 1 77 and 1 = (1 (6-15) - p)H , where NH is the number of hazardous-material cars in the train . Once these conditional parameters are derived, by using Equations (6-12) and (6-13) , the parameters of the gamma distribution may be obtained . The gamma distribution is: p(X) (xf)) -I exp (-AX) , (6-16) where denotes N ' given that N 1. x HO H � The parameters and can be obtained from the following A n expressions : E(N O N > 1) .. H H " :I = I (6-1 Var(N O N > 1) i) H I H • One now has an estimate of the complete probability distribution of the number of hazardous material cars derailing, conditional on there being an accident to a train carrying hazardous-material cars . However, this is a continuous distribution, whereas the variable NHO is discrete--it can only take integer values . To overcome this problem, one may determine the probability that J (some integer) by integ NR = rating the area under the probability distribution from J - S to J + 1 - where is a fraction smaller than one . a, a Then: P(N OIAccident and N > 0) area from 0 to (1 R = H = - a) - P(N = 1 Accident and N > 0) = area from (1 to (2 - R 1 H S) S) . and so on. 78 The value of was obtained by matching P(N 0) to the S HD = historical data. On this basis, S was found to have a value of 0.65. E. REFERENCES I 1. Parzen, E., "Stochastic Processes, Holden-Day , Inc. , I 1962. 2. Drake, A. W., IIFundamentals of Applied Probability Theory, II McGraw-Hill Book Company , 1967. 79 7 • RELEASE PROBABILITY A. INTRODUCTION A factor of considerable interest in any risk analysis model is the probability that a derailed or damaged hazardous-material car will release all or part of its contents . If: number of hazardous-ma terial cars derailing or damaged, and = number of hazardous-material cars releasing all or part of their contents, then the release probability is defined to be: q E (7-1) 0 (::) It is reasonable to assume that the release probability depends on speed; it is therefore written q(v) . Historical estimat es of its value are present ed in the following sections . B. DERAILMENTS From the FRA accident data base, empirical distributions of q (v) for derailments on mainline and yard track tl1ere tabulated (Tables 7-1 through 7-3) . An initial investigation was made to see whether a common q(v) function would be appropriate to all track types . Chi-squared tests (and test on the differences in proportions where appropriate) were performed on the number of cars releasing and not releasing for mainline, yard, and other types of track. The only sign ificant differences are indicated below: 1. On comparing mainline and yards in the 16- to 20-mph range, 57 out of 219 mainline cars released, while o out of 12 yard cars released. The test statistic for the proportion difference is : 80 TABLE 7-1. RELEASE PROBABILITY : DERAILMENTS (1975-1977) v Number of HM Number of HM (mph) Cars Releasing Cars Derailing q(v) 0-5 53 746 .07 6-10 58 495 .12 11-15 9 147 .06 16-20 61 241 .25 21-25 36 221 .16 26-30 51 176 .29 31-35 32 122 .26 36-40 48 179 .27 41-45 25 76 .33 46-50 31 81 .38 51-55 14 33 .42 56-60 7 14 .5 - 61-65 - - 66-70 1 23 .04 81 TABLE 7-2 . RELEASE PROBABILITY : MAINLINE DERAILMENTS (1975-1977) Number of HM Number of HH v (mph) Cars Releasing Cars Derailing q(v) 0-5 11 117 .09 6-10 34 283 .12 11-15 7 112 .06 16-20 57 219 .26 21-25 36 215 .17 26-30 51 176 .29 31-35 31 121 .26 36-40 47 172 .27 41-45 25 74 .34 46-50 31 80 .39 51-55 14 33 .42 56-60 4 10 . 40 61-65 - - - 66-70 1 23 .04 71-75 - - - 76-80 - - - 80 - - - > 82 TABLE 7-3. RELEASE PROBABILITY : YARD DERAILMENTS (1975-1977) v Number of HM Number of HM (mph) Cars Releasing Cars Derailing q(v) 0-5 26 502 .05 6-10 18 173 .10 11-15 2 17 .12 16-20 - 12 0 21-25 - 1 0 26-30 - - - 31-35 1 1 Small sample 36-40 - - - 41-45 - - - 46-50 - - - 51-55 - - - 56-60 - - - 61-65 - - - 66-70 - - - 71-75 - - - 76-80 - - - > 80 - - - 83 57 ° - 219 12 ; 2.04 p(l - + p (l - 219 p) 12 p) wh ere .... 57 + ° p = = 0.25, 219 + 12 wh ich is significant at 4 percent . 2. In the 0- to 5-mph range , derailments on "o ther" types of track show a higher release probability (although mainline and yards are not significantly dif ferent) , as shown in Table 7-4. Apar t from these speed ranges, there are no significant differences , and thus the ov erall distribution of Table 7-1 was used . Several functions were tes ted as models for q(v) . (For simplicity, only one- and two-parame ter func tions were tested .) Th e data show a sharp decline in release frequency for the highest speed class, although this is based on only 23 derailments out of a total of 2554 derailments. Therefore, the effect of this apparent outlier point should be miti gated by applying a weighted regression , where the weights are the number of derailments . The following one-parameter function was within 2.22% of the mini mum error and was chosen to simplify the modeling. This function is : O.5 q(v) = 0.045 v • (7-2) The total weighted sum-of-squares around the mean was 0.1390, which yields a percentage variation explained of 74% . A graph of q(v) and the empirical values are presented in Figure 7-1. 84 TABLE 7-4. RELEASE PROBABILITY COMPARISON IN THE o TO 5 MPH RANGE FOR VARIOUS T��CK TYPES Cars Cars Location Releasing Not Releasing Total Cars q(v) Mainline 26 476 502 0.052 Yard 11 106 117 0.094 Others 16 111 -127 0.126 TOTAL 53 693 746 0.071 85 • 0.4 • O.5 • q(v) = 0.045v 0.3 • • Release 0.2 Probability � • 0.1 • • 10 20 30 40 50 60 70 Derailment Speed (mph) FIGU RE RELEASE PROBABILITY SHOWING RAW DATA AND ANALYTICAL REPRESENTATION 7-1. q(v). C. COLLISIONS Estimation of q (v) for collisions was hampered by the limited amount of data for hazardous materials releases in collisions. Table 7-5 presents the da ta for the 1975-1977 period. Although the overall ratio of the number of cars releasing to the numb er derailed or damaged (i.e. , the release probability) of 0.129 is somewhat less than the comparable value for derailments, it is believed that this is partly due to the lower velocities that are generally observed in collisions and partly because of the practice of lo cating hazardous material cars away from the ends of trains. Utilizing the functional form of q(v) for derailments , one would expect 15 cars to release out of 205 in the 0- to5-mph range and 4 out of 33 in the 6- to 10-mph range . Historical data are in reasonable agreement with these expecta tions (considering the sparseness of the data) and , thus , the identical form of q(v) is recommended for collisions as for derai1ment� . 87 TABLE 7-5 . RELEASE PROBABILITIES FOR COLLISIONS (1975-1977) v Number of HM Number of HM (mph) Cars Releasing Cars Derailing q(v) 0-5 19 205 .093 6-10 1 33 .030 11-15 3 7 .078 16-20 0 1 .000 21-25 1 4 .250 26-30 4 4 1.000 31-35 1 3 .333 36-40 3 5 .600 41-45 0 1 .000 46-50 3 7 .428 71-75 0 1 .000 Overall 35 271 .129 88 8. NllMBER OF HAZARDOUS -HATERIAL CARS RELEASING THEIR CONTENTS INTRODUCTION A. The distribution of the number of hazardous-material cars releasing th eir contents is analyzed in this chapter. Th is distribution depends on the distribution of the number of hazardous-material ,cars derailing , N , and on the release probability , q. The issue of how HD mu ch of hazardous material is released is dealt with in the Chapters 9 and 10. B. NUMBER OF HAZARDOUS-MATERIAL CARS RELEASING If a hazardous-material car derails , the probability that it will release its contents is termed the "release probability" and is denoted by q(v) , or q. Once such a release occurs, there is a probability 'r' that the in itial or primary release will cause a secondary release due to fire from 'k' additional cars , and (1 - r) that no secondary release occurs . Thus , for one derailing hazardous-material car, one has: Prob (1 car releases) = q(v) (1 - r) , and Prob (1 + k cars release) :::0 q(v) r. Thus, given one derailing hazardous-material car, the expected number of releasing cars is : . - q) + 1 . (1 - r) + + k) . q r o (I q • (I • :::a q{l + kr) . (8-1) The variance can be derived in a similar way : 2 2 2 = q(l + 2kr + k r) - q (1 + 2kr) • (8-2) 89 On the assumption that secondary releases are infrequent, it is no t unreasonable to assume that the secondary releases caused by each primary release are independent . Then,gi ven � hazardous-material HD cars derailing, the mean and variance for the number of cars releasing are: and When Equations (8-1) and (8-2) are introduced into these expressions , one ob tains : (8-3) and (8-4) Repeated application of Equations (6-1) and (6-2) leads to: E(N ITT, TC, AT, AC) (1 kr) E(q ITT, TC, AT, AC) (8-5) R = 'II'H + �ID and 'II' (1 2kr k 2 lTT, TC, AT, AC) Var(N !TT, TC . AT . AC) = + + r) E(q � R H D 2 2 + (1 + kr) Z(q TT, TC, AT, AC) + 'II'� { aN D + Var(q ITT, TC, AT, AC) • (8-6) N D } 90 The conditional distributions of the numb er of hazardous-material cars derailing, derived in Chapter 6, have been us ed here. Finally, the velocity-dependent expressions derived in Chapter 4 for and and in Chapter 7 for q are introduced into Equations �_ a� (8-5) Nnand (8-6)·' n to yield: E(N ITT, TC, AT, AC) rr (l + kr) df E(vITT, TC, AT , AC) , (8-7) R = H and 2 Var(N ITT, TC, AT, AC) rr (l + 2kr + k r) df E(vITT, TC, AT , AC) R = H 2 2 1.5 {(1 - m� - 1} (1 kr) df E(v 1TT, TC, AT, AC) + oR 'R) + 2 2 2 2 2 + rrH (1 + kr) { (e + d ) f E(v ITT, TC, AT, AC) 2 2 2 - d f [E(v ITT, TC, AT , AC) ] } • (8-8) The procedure described in Chapter 6 for fitting the gamma distri- bution and making it discr�te can be applied to Equations (8-7) and (8-8) , if a discrete probability distribution for NR is desired . The necessary conditional means of the velocity are shown in Table 8-1. As in Chapter 6, the data for collisions are conditional on at least one car derailing or being damaged in the collision . Th e values of the parameters d, e and f are summarized in Table 8-2. C. VALUES FOR r, m AND k GH Data on 'r' are hard to come by. Some information is available in an Association of American Railroads/Railway Progress Institute (AAR/RPI) Tank Car Safety Research and Test Project Report [1] : Number of accidents with a release 434 Number of accidents with a secondary release 43 91 0.5 1.5 2 8-1. VALUES AND TAULE MEAN 01-' v , v, v. v Mean Va lue of 0.5 1.5 2 Accident Group v v v v Yard dera ilments 1.89 3.96 9.S3 27 .3 Mainline derailments 4.03 18 .9 98.5 554 Mainline Class 1 de railments 2.67 7.95 26 .5 98 .6 Mainline Class 2 derailments 3.68 14.9 64 .1 290 1.0 N Ma inline Class 3 derailments It .3B 21.3 III 604 Mainline Class 4 derailments 5.17 29 .7 182 1150 Mainline Classes 5 and 6 de railments 5.81 37 .6 257 1814 Track-caused yard derailments 2.28 5.86 12 .7 32.9 Track-caused mainline derailments 3.53 14.6 68.0 347 Yard collisions 0 1. 74 3.29 7.23 20.6 (N > ) Mainline collisionsD 0) 3.06 12.6 63.6 362 (N > Ma inline Class 1 collisD ions > 0 2.15 5.57 17 .5 64 .6 (N ) Mainline Class 2 collisions D 0 2.73 9.09 35.3 152 (N > ) Mainline Class 3 co llisions J) > 0 3.26 1].6 66.8 358 (N ) Mainline Class 4 collision s D > 0 3.51 16.5 91.9 555 (N ) Ma inline Classes 5 6 collisionD s 4.1B 23.5 152 104 3 & (N > 0) n TABLE 8-2 . VALUES OF REGRESS ION CONSTAI.'lTS Constants Accident Category d e f Mainline and yard derailments 1. 7 2.7 0.045 (All causes) Mainline and yard derailments 2.1 2.7 0.045 (Track-caused) ��inline and yard collisions 1.25 2.3 0.045 (Given at least one derailing car) Note : O.S E(NO) - = dv �o Var(N ) - 0'2 = ev o NO O.S q = fv 93 Thus : r = 43/434 = 0.1 • This estimate must be treated with caution. It is likely to be high because the AAR/RPI project concentrated on severe hazardous material accidents, wh ich generally have a higher value of r. Historical data are not available for the parameters m and k. GH They were assigned values of m 4 and k = 2 on the basis that these G = resulted in the best fit betweefi the predicted and historical values of the mean and variance of NR, for mainline derailments. With a value of r = 0.1, �d for m = 4, k = 2, predicted values are : aa 0.0312 = Predicted values for �R mainline derailments 2 0.0745 o = N R The historical values are : � 0.028 Historical values for mainline derailments = 0.072 It may be seen that the historical and predicted values of and 2 � R o are fairly close. N R D . QUANTITATIVE RESULTS FOR MEANS AND VARIANCES The velocity moments given in Table 8-1 were introduced into Equations (8-7) �d (8-8) , along with the parameter values shown in Table 8-2. Using r 0.1, k 2 and m 4, the estimates of the mean = = G = and variance of NR shown in Table 8-3 w�re obtained. 94 TABLE 8-3 . PREOICTEO MEAN Al.� O VARIANCE FOR THE NUMBER OF CARS RELEASING THEIR CONTENTS Accident Group �R Yard derailments .0062 .01172 Mainline derailments .0312 .0745 Mainline derailments , Class 1 .0100 .0205 Mainline derailments, Class 2 .0255 .0567 ::-Iainline derailments, Class 3 .0413 .0984 Mainline derailments, Class 4 .0461 .1170 Mainline derailments, Classes 5 & 6 .0621 .1660 Track-caused yard derailments .0102 .0192 Track-caused mainline derailments .0297 .0680 Yard collisions, NO > 0 .0056 .0104 �tainline collisions, No > 0 .0170 .0403 ::-!ainline Class 1 collisions, ND > 0 .0075 .0152 �ainline Class collisions , N .0122 .0265 2 O > 0 ::-lainline Class 3 collisions, ND > 0 .0184 .0431 Mainline Class 4 collisions , NO > 0 .0223 .0550 Mainline Classes 5 & 6 collisions, No > 0 .0317 .0836 95 It is important to note the following conditions on these means and variances: They are no t conditional on the train carrying at least • one hazardous-material car. Thus , means and variances conditional on having NH 1 must be developed for the gamma-fitting process before� distributions of N are developed. The process is described in Chapter R6; and For collisions, the values are conditional on at least • one car having been derailed or damaged in the accident . E. REFERENCE 1 . Railway Progress Institute/Association of American Railroads Tank Car Safety Research and Test Proj ect, "Final Phase 01 Report on Accident Review,1I Review No. RA-01-4-16 , June 1972 . 96 9. AHOUNT OF HAZARDOUS K.<\TERIAL D D RELEASE : MEAN AN VARI.A�'lCE A. INTRODUCTION The quantity of hazardous material released in an accident , denoted by is analyzed in this chapter . Its distribution is �, determined by the distributions of the number of cars releasing (NR) H and of the amount released per car , a Re istorical data for the dis tribution of aR are presented . These data are then used, along with distribution of NR (obtained in Chapter 8) to ob tain analytical results for the means and variance of �. An alternative , more complex procedure is used in Chapter 10 to obtain numerical results for the dis tribution of AR• While these numerical results are more accurate, the analytical results presented in the following paragraphs are more generally useful and flexible, and provide more insight. B . QUANTITY RELEASED PER CAR When a hazardous-material car releases its contents; it does not necessarily release all of them. In many instances , minor releases occur due to damage to fittings, but nevertheless these releases have to be reported to the FRA and the MTB . To determine how much material is released per car , MIB data were analyzed. Since it might be expected that the qua ntity released per car is a function of speed, the mean and variance of aR were plotted as functions of speed, as shown in Figure 9-1 . Because of the sparseness of the data, it was no t possible to develop separate plots for releases conditional on track class , track type , and so forth. Both the mean and variance appear to increase with an increase in velocity . Unfortunately , there is also a great deal of random fluctuation in the data, primarily because the sample size is small . Statistical tests were performed to compare these statistics for 97 Variance Mean x 6 20000 400 10 I� I \ I \ Mean I \ 300 x 106 15000 " A I ", \ ", \ \ \ '" I., \ \ 200 x 106 10000 I � I / I 100 x 106 I I I �/ V o 5 10 15 20 25 30 35 40 45 50 55 60 Velocity, mph FIGURE 9-1. MEAN AND VARIANCE OF AMOUNT RELEASED PER CAR 98 releases in accidents occurring at less than and greater than 5 and 10 miles per hour (mph) . Table 9-1 presents the mean and variances for these classi fications and Table 9-2 presents the resul ts of the statistical tests. For mo deling purposes , a constant value of variance with respect to velocity was assumed. This value is equal to 1.31xl08 gal2 The assumption of a constant rather than a slight trend does not affect any of the results in a significant manner. Furthermore, the signifi cance test does not strongly indicate that there is variation with respect to speed. For the means there does appear to be a trend with respect to speed. The relationships used are: ma 2 x 10 v 3 0 . 5 ga11 ons , R = (9-1) 28 1.3xlO (gallons) 2 a = • (9-2) aR It should be noted that th e model assumes that the amounts released from each releasing car are independent and identically distributed . It is difficult to support this assumption, because of the limited amoun t of data , but this is reasonable from a physical point of view. rhere were only a limited number of accidents (25) for which releases were recorded and in which there was more than one car releasing . (This was due to the limited amount of Materials Transportation Bureau (MTS) data, which are presented in Figure 9-2.) Although the mean and variance of the amount released per car in thes� multi-car releases show slight increases over the mean and variance of amount released in one-car accidents, tests show no significant differences . If there is a difference, the statistics do not show it, because of the limited amount of data. It was assumed , therefore, that the amounts released per car ar� independent, identically distributed random variables . 99 H TABLE 9-1. MEANS Al.'l D VARIANCES OF T E AMOUNT RELEASED PER CAR (aR) FOR SELECTED VELOCITY CATEGORIES, IN GALLONS Velocity Category Mean Variance (millions) 0-5 3767 72 0-10 5175 10 7 > 5 11044 133 >10 11664 140 TABLE 9-2. TESTS OF SIGNIFICANCE FOR VARIATIONS IN THE MEAN A..�D VARIANCE OF THE AMOUNT RELEASED PER CAR Comparison t-Va1ue F-Valu* e Significance Means: 0-5 vs > 5 3.79 Very significant Means: 0-10 vs > 10 3.57 Very significant Variances : 0-5 vs > 5 1.85 '" Ii; Variances: 0-10 vs > 10 1.31 Not significant 100 0.4 0.4 N 1 = H R NH R 2 = (Total : 100) (Total : 17) 0 . 3 0.3 0.2 0.2 0. 1 0.1 0 0 0 ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: 0 ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: .- ..Iii: .- e It) e It) e e 0 e I It) e It) e 0 e - .- .- I .- I I It) e e N 0 e .- .- .- .- .- N I I I N I .- I I .- .- .- .- .- .- 0 e I .- .- I I .- I e.- e .- .... e e 0� e ... e e e if .- .- e e e � � It) � It) e It) e It) � 8 .... 8 .- &N 0 N a g e g g gallons gallons �, �, 0.6 - 0.4 - N NH R H R 3 = = (Total : 4 (Total : 7) 3) O.S - 0.3- r+- r+ ..... 0.4 - 0.2- 0. 3 - 0. 1 0.2 - 0 ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: .... It) .- e It) e e e I I .- N It) e :3I .- .- I I I .... 0.1 - .... e e .... .- .- I �I e .- .- .- 8 It) e It) 8, 8 a &N 0 0 0 � ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: ..Iii: gallons .- It) e It) e e e 8...... ('II It) e I I e.- I .... .- I I I ('II �, .- e e .- .... .- I I .- e e e e .- .... e � � 0 It) e It) � .... ('II a f5 8.- gallons �, FIGURE 9-2 . DISTRIBUTION OF AMOUNT RELEASED AS A FUNCTION OF THE NUMBER OF CARS RELEASING. (Not shown are one accident with N 5 and A 100-200K HR co R '" gallons, and another with N and A SO-100K gallons.) HR '" 6 R '" 101 C. AMOUNT RELEASED PER ACCIDENT The amount released from NR cars has a mean and variance given by: (9-3) and = NR a2 (9-4) a R The means and variances of conditional on an accident having occurred' in a given group (defined� by TT, TC, AT, and AC) can be obtained by combining Equations (8-5) and (8-6) for the mean and variance of NR with Equations (9-3) and (9-4) , using the process defined by Equations (6-1) and (6-2) . The resulting expressions are: and Var(A !TT, TC , AT, AC) � (l + E(� q\TT, TC, AT , AC) = H R kr)a a2 a D 2 2. E ( � ma q ITT, TC, AT, AC ) D R + � (l + kr) E(� m q TT, TC, AT , AC) H • N 2 2 { D a2 R 21 + Var(� m q ITT, TC, AT, AC) (9-6) D • � } 102 When the following general forms are introduced into Equations (9-5) and (9-6) : 0.5 q = f v 0.5 m = v aR g One obtains the following expressions: 1 E( TT , Te, AT, AC) � (l kr) dfg E (v . S TT, TC , AT, AC) (9-7) = H + �I I and Var(N TT , TC, AT , AC) � (l kr) dfh E(v TT, IC, AT , AC) = H + R I I 222 + � (l 2kr + k r) dfg E(v TT , IC, AT , AC) H + I 2 3 + 'i( l + kr) fg(efg + d) E(v TT, TC, AT, AC) 1 I - dfg [ E(v1 • S TT , TC, AT , AC) ] 2 (9-8) I ! Values for d, g and h are shown in Table 9-3 Values for the e, f, . conditional moments of velocity are presented in Table 9-4. 103 TABLE 9-3. VALUES OF VARIOUS REGRESSION CONSTANTS Accident Constant Category d e f g h 3 8 Mainline and 1.7 2.7 0.045 2xl0 1.3xlO Yard Derailments (All causes) 3 8 Hainline and 2.1 2.7 0.045 2xlO 1.3xlO Yard Derailments ( Track-caused) 3 �in and 1.25 2.3 0.045 2xl0 1.3xlO 8 Yard Co llisions Note: dvO.5 � = 2 D = ev aN D O.s q = iv 0.5 = gv ma R 2 = h 104 TABLE 9-4. MOMENTS OF 11lE DI STRIBUTION OF ACCIOENT SPEEOS Expec ted value of Acciden t Croup 0.5 1.5 2 2.5 3 v v v I v I v v Yard derailments 1.89 3.96 9.53 27.3 95 .5 414 Mainline derailments 4.03 18.9 98. 5 554 3300 20500 Ma inline Class 1 derailmen ts 2.67 7.95 26 .5 98.6 412 1920 Mainline Class 2 dera ilnlents 3.68 14.9 '64 .1 290 1360 6560 Mainline Class 3 derailments 4.38 21. 3 111 604 3420 19900 Mainline Class 4 derailments 5.17 29.7 182 1150 7480 49700 Mainline Class 5 and 6 derailments 5.81 37.6 257 1814 13044 95950 Track-caused yard derailme nts 2.28 5.86 12.7 32.9 99.1 380 Track-caused mainline derailments 3.53 14 .6 68.0 347 1890 10700 .... o Yard collisions , N 0 1. 74 3. 29 7.23 20.6 83 .6 480 VI o > Mainline collisions , N 0 3.06 12.6 63.6 362 2220 14200 o > Mainline Class 1 collisions , N > 0 2.15 5.57 17.5 64 .6 269 1220 O Mainline Class 2 collisions , N 0 2.73 9.09 35.3 152 702 3400 O > Mainline Class 3 collisions , N 0 3.26 13.6 66.8 358 2030 11900 O > Mainline Class 4 collisions, N > 0 3.51 16.5 91.9 555 3510 22900 O Mainline Class 5 and 6 collisions , N 0 4.18 23.5 152 1043 7425 53750 U > O. QUANTITATIVER ESULTSFOR MEANS ANO VARIAI.'iCES Equations (9-7) and (9-8 ) may be used to obtain numerical expressions for the mean and variance of AR. This was done, using the 9-3 -4 0.1, contents of Tables and 9 and also the parameter values r = 9-5 . k = 2 , and mGH = 4. The results are shownin Table E. THE GANMA-FITTING PROCEDURE To fit an accurate gammadist ribution to the distribution of AR' it is necessary to recognize the significantprobab ility massat = . � O This mass arises partly from the large probability (1 - PH) that the train does not carry hazardous materials, but also from the probability that no hazardous-material cars derail, and that even if they do derail, they do not release their contents. It is preferable to obtain means and variances for AR that are conditional upon a release occurring > 0) (i.e., AR before fitting the gamma distribution. 1. Probability of Release The probability that a release occurs, given an accident, is denoted by PR: > (9-9) PR = P(� O!Accident). The probability of a release can be derived as follows: If N cars derail, (NO/GH) blocks derail. If a block derails, the probabilityo that at least one car in the block releases is: 1 - 1 P(none releases) = - P(given car does not releaSe) GH � 1 - (1 = - q) (9-10) Thus, the probability that a hazardous-material car releases, given that a block derails is: 106 TABLE 9-5. MEAN A!.'ID VARIANCE OF THE A...'10UNT RE LEASED PER ACCIDENT 2 m Accident Group � a� Yard derailments 30.33 1.18 Mainline derailments 331. 87 13.73 Mainline derailment s, Class 1 67.84 2.45 Mainline derailments, Class 2 224 .50 8.09 Mainline derailments, Class 3 437.70 17.46 Mainline derailments, Class 4 575.20 25.43 Hainline derailments, Class 5 and 6 866 .00 42.40 Track-caused yard de railments 49 .80 1. 86 Track-caused mainline derailments 283. 20 5.75 Yard collisions , N 0 24.88 1.05 D > Mainline collisions, N 0 171. 60 7 . 18 D > Mainline Class 1 co llisions , N 0 47.20 1. 74 D > Mainline Class 2 co llisions , N 0 95.40 3.46 D > Ma inline Class 3 collisions, N 0 180 .40 7.16 D > Mainline Class 4 collisions , N 0 248.00 10.63 D > 5 6 0 410.40 19 .47 Mainline Classes and collisions , N D > 107 P(given block is hazmat) P(one re1eases l hazmat block) Thus, the probability that no hazardous-material car releases is: = P(no cars re1easelb1ock derails) GH (9-12) = 1 - (1 - �H + �H q) For a given value of one can develop a binomina1 expansion as follows: ND, P(re1ease) = 1 - P(no release) GH ::: NGHD �H [ 1-(1 - q) ] _ ::: 1/2 (1 _ 1 ['H q) GH [NDG ] [NGD f H H ] 1 -2 '" (9-13) � q (7TH q) [ ] H - 2" �:: y )]+ where :: (� q '" 1 1 - (v - [ q rH • (9-14) 108 In the expansion, the first termdom inates the expression, and thus, the first term alone is an excellentappro ximation. In addition, at a given velocity, by taking the expected value of NO' one has: �o > (9-15) IAccident) = q • P(� O T "" 'lTH H If a distribution of speeds is being used, then the expected value of Equation (9-1S) must be computed. Now: G 1 - (1 - H q = q) 1 - (1 0.045 vO•S) G 7) _ H (From Chapter Consequently, as a first approximation, q varies as the square root of v. As n. is also proportionalto the square root of v (Chapter 4) , theNO ri ght hand side of Equation (9-1S) varies approximately as v. Thus, if v is takenfro m a distribution, the velocity that should be used in Equation (9-15) is E(v). Modified Meanand Variance for AR 2. The procedure for obtaining a mean and variance for AR given that A > ° parallels the procedure described in Chapter 6. The resulting expR ressions are: E(AR\TT, Te, AT, AC; AR > 0) (9-16) 109 and Var( TT, TC, AT, AC; A > 0) �I R ::: (9-17) where m ::: E(A- TT, TC, AT, AC) AR --aI is given by Equation (9-7) and in Table 9-5 , and a 2 ::: Var(A- TT, TC, AT, AC) AR --aI is given by Equation (9-8) andin Table 9-5 . Estimated values of are PR given in Table 9-6 . Once the conditional meanand variance are obtained, the remainder of the procedure for obtaining a gamma distribution is identical to that presented in Section 6D. However, the distribution of AR does not need to be made discrete (while those of NH or NR do), since is a-conti nuous variable. D � 110 TABLE9-6 . ESTIMATED PROBABILITYTHAT A HAZARDOUS MATERIALIS RELEASED, GIVEN AN ACCIDENT Accident Group PR Yard derailments 0.0043 Mainl��in1ineine Classderailmen 1 derailmts ents 0.00670197 ��in1ine Class 2 derailments 0.02600167 HainlMainliine ClClassass 43 derderaaiillmenmentsts 0.0281 Mainline Class 5 and 6 derailments 0.0368 Track-caTrack-cauusedsed mainlineyard der ailmederailntsments 0.0.00107192 Yard collisions, ND > 0 0.0039 ��in1ine collisions, ND > 0 0.0134 Mainline Class 1 collisions, NO > 0 0.0063 �inline Class 2 collisions, NO > 0 0.0101 }�inline Class 3 collisions, NO > 0 0.0146 Hainline Class 4 collisions, N > 0 0.01 2 5 O 7 Mainline Class and 6 collisions, NO > 0 0.0237 111 10 . AL"1RELEASED0UNT OF PERHAZARDOUS ACCIDENT-MATE: DISTRRIALIBUTION A. INTRODUCTION This chapter provides quantitative results for the distribution of the amount of hazardous material released per accident, for parti cular grouping of accidents. These results are not based�, on the gamma fitting procedure discussed in Chapter 9. Whilethat procedure provides greater flexibility for general application, it was decided that, for predetermined accident groups, greater accuracy could be obtained by using the procedure described below. B. THE PROCEDURE Instead of computing the mean and variance of one can compute the actual distribution of by starting with the estimat�, ed discrete distri bution of the number ofAR cars releasing, P(NRjTT, TC, AT, AC) . Then: P(A ITT, TC, AT, AC) = co P(N = MITT, TC, AT, AC) (a;)M R M=oL R where (a* )'M denotes the M-th convolution of the distribution of the random variaR ble a with itself. The distribution of a (which is the amount released perR car) is available from historical Rdata ; certain parameters of this distribution are shownin Figure 9-1. C. RESULTS The distribution of the obtained by applying the method � described above are presented in Figures 10-1, 10-2, 10-3 and 10-4 . The following conditions apply to these distributions: • All are conditional on an accident occurring to a 0) ; train carrying hazardous-material cars (Le., NH > 112 0 10 ,------. MD MC - - _ _ YO YC S MD = Mainline Derailments 1 0-2 YO Yard Derailments 1\ = :I: Z Me Mainline Collisions - = Given N � 1) X YC Yard Collisions D /\\ = } a:: � > .:: :c � 3 ...0 1 0- C1. 5 10- �------�------�------� 2 1 0 x (gal) FIGURE CUMULATIVE DISTRIBUTIONS OF AMOUNT RELEASED, A , GIVEN 10-1. R THAT NH > O. (ALL MAINLINE AND YARD COLLISIONS AND DE RAI LMENTSI. 113 TM D TYD TMD ::;; Track-Caused Mainline Derailments -2 10 TYD ::;; Track-Caused Yard Derailments 1\o :I: -.Z x ,\"', 4 10- 5 �______10- � � � 2 3 4 5 10 10 10 10 (gal) x, FIGURE CUMULATIVE DISTRIBUTIONS OF AMOUNT RELEASED, A , GIVEN 10-2.. R THAT N O. (ALL TRACK-CAUSED MAINLINE AN D YARD H > DERAI LMENTS)_ 114 MD 5i6 =::::::: --::: MD 2 -::: �83-- --::::=:; D -- M 1 - ___ MD Mainline Derailments on Class Track 1 = 1 MO Mainline Derailments on Class Track = MD 2 Mainline Derailments on Class 2 Track 3 :::: 3 10-2 MD Mainline Derailments on Class Track /\0' 4 = 4 MD = Mainline Derailments on Class Tracks :x:: 5/6 & 6 ....2 5 X'\ \ 10-4 ______10-5 �______� � � 102 X. (gal) FIGURE EFFECT OF TRACK CLASS ON THE CONDITIONAL DISTRIBUTION 10-3. OF AMOUNT RELEASED FOR MAINLINE DERAILMENTS l1S 0 10 l I MC 5/6 1 10- MC 4 MC 3 MC 2 MC 1 MC 1 = Mainline Coll isions on Class 1 Track 0- MC 2 = Mainline Collisions on Class 2 Tracie /\ MC 3 = Mainline Collisions on Class Track :I: 3 MC 4 = Mainline Collisions on Class 4 Track .....Z MC = Mainline Collisions on Class 5 6 Tracks x 5/6 & I i I -4 1 0 I IIi I I I 5 10- 2 3 4 5 10 10 10 10 (gal) X FIGURE EFFECTS OF TRACK CLASS ON TH E CONDITIONAL DISTRIBUTION 10-4. OF AMOUNT RELEASED FOR MAINLINE COLLISIONS 116 • The distributions for collisions are additionally damagcondited;ional and on at least one car derailing or being A > • Thise dist condriitibutonions is noaret nonecest condsaryit, ionalsince on the ha vingdistri utionsO. artheeir fully means com anputd varianced, ratheesr. than being estimated fr§om To facilitate the analysis of small releases, Table 10-1 presents 0) . the value of P( = Accident and N > Theseare the values to � O I H which the curves in Figures 10-1 through 10-4 tend as x tends to zero. D. ACCURACYC HECK Data on the amountrele ased per accident were obtained from the �1aterials Transportation Bureau (HTB) data base, and are compared 'Nith the estimates resulting from the "simple" (parameter estimation and gamma-fitting) model of Chapter 9 and the "complex" (parameter estima tion, gamma-fitting, and convolution) model of Chapter 10 and shown in Table 10-2. Significant differences exist: the historical data show that the probability that the amount released is less than 1000 gallons is 0.37, while the models provide estimates of 0.22 and 0.27. There is reason to believe that the differences may result from biases in the data, resulting principally from misSing data regarding the amount released in some large accidents. An alternative test was constructed by using historical data for the distributions of both the number of cars releasing and the amount released per car in a convolution pro cedure, to estimate a synthetic distribution for the amount released per accident. This distribution is shownin the last column in Table 10-2 . It may be seen that, in comparison with this historically based computation, the complex model provides excellent results, while the simple model is reasonably accurate. E. APPLICATION OF PROCEDURE The following is a step-by-step summaryof how to obtain a distri bution of the amount released. 117 10-1. H = TABLE PROBABILITY T AT AR a GIVEN AN ACCIDENT WITH NH > a & Accident Group P(� = OIAccident NH > a Yard derailments 0.924 Hainline derailments 0.796 Mainline Class 1 derailments 0.970 Mainline Class 2 derailments 0.816 Mainline Class 3 derailments 0.787 Mainline Class 4 derailments 0.752 6 0.711 ��inlineClass 5 & derailments Track-caused yard derailments 0.886 Track-caused mainline derailments 0.776 0) 0.952 Yard collisions eN > D 0) 0.880 Hainline collisions (N > 1 D 0) 0.928 Mainline Class collisions (N > Mainline Class 2 collisions (ND > 0) 0.901 3 D 0) 0.876 Mainline Class collisions eN > Mainline Class 4 collisions (ND > 0) 0.863 5 & 6 D 0) 0.826 Mainline Class collisions (ND > 118 TABLE 10-2. COMPARISONS OF TABULATEDRELEASE DISTRIBUTIONS GIVEN > 0 FOR DERAILMENTS � r � > 0) l p (� 2 XI� 3 H 4 ( allons) EmpObse irirvations cal MoSimpdelle ModCompellex Basedistor Comica11putaty ion X G 1,000 .37 .22 .27 .29 5,000 .49 .43 .36 .39 10,000 .61 .59 .47 .50 25,000 .83 .83 .74 .78 50,000 .92 .95 .95 . 965 100 ,000 .99 .996 .996 .994 1130 �ITB accidents. 2Mode1 described in Chapter 9. 3Model described in this chapter, Section B. 4 usfores numb convoerlut of ioncars pr ocreleedureasing, incorpoas wellra asti ngthe his amotountric alrele disastedribut perio nscar . 119 1. Choose the track type, TT (yard, main); Track Class, TC (1 through 5 & 6; for main track only); Accident Type, AT (a(derailll causmenests andand trcoackllisi causons)es); ; and accident cause, AC 2. Determinethe accident rate from the data in Chapter 3; 3. Dacetcierminedent ratthees ewithxpecte esd tiaccidmatesent of freexposuquencyre ; by combining 4. For an accident, determine theprobab ility PH that the trainthat at carries least onehazardous car is ma derailedterials , orand damage for d,coll Pisions' Va, lues CD 5; for PCD are presented in Chapter 4 and for PH in Chapter S. 0 Given an accident, the probability that AR = is given by: (1 - PR) where PR is the probability of a release, given in Table 9-6 ; 6. Given an accident, the distribution of A is obtained by multiplying the curves in Figures 10-1 tnRrough 10-4 by PH for derailments and by PH PCD for collisions; and 7. Given N accidents within a group, the probability distri bution for .� is obtained by taking the N-th convolution of the distrIbution obtained in step 6 , above. 120 11. ERROR ANALYSIS OF THE RISK ESTIMATES A. INTRODUCTION An invariable concernin performing a risk analysis is the accuracy of the risk estimates that are developed. This concernex presses itself in two different ways: 1) howIf thelikely predicte is itd rithatsk theis lowrisk in is some und aberstsolateuted, senandse, oneby how is munoch?t bei Theng lulled desire intohere a isfalse to make sense su reof that security. 2) alarmisConverselyt: to, theremake suris ane, whenequal highdesire levels not ofto berisk are thpreem.dicted , that one is not grossly overestimating In the literature on risk analysis, this concern is typically addressed by developing "confidence bounds" on estimates of risk. This termis a misnomer, because the bounds are not statistically valid ones, with an associated confidence level. The bounds are usually developed by a series of qualitative, intuitive arguments, which have a ring of plausibility to them, but which are not capable of proof. Despite this shortcoming, they are valuable because they provide a measure of insight into the accuracy--or lack thereof--of the estimates of risk. In the present project, an attempt was made to develop rigorous confidence bounds, with some measure of success. Qualitative and quantitative reasoning had to be combined to develop useful estimates of error. The overall process is described here, along with recommended bounds for the probability distribution of the amount released, This description is preceded by a discussion of various sources �.of error in the risk estimation procedures developed in this report. 121 B. SOURCES OF ERROR 1. Inadequate Historical Experience The risk estimates are based , to a large extent , on historical data regarding releases of hazardous materials . To the extent that these data are sparse, the possibility exists that they represent a biased sample, and that future experience may be different. There is no rigorous way to quantify this error, except through analytical modeling which, of course, begs the whole issue of the accuracy of analytical models . 2. Sys tematic Errors in Historical Data Systematic errors may exist in historical accident data. Possible examples include misreporting of accident cause and train speed , and the absence of data on the amount of hazardous materials released in some large accidents. To the extent that these errors can be measured , they can be corrected for , and have been in this report. If only qualitative information regarding the extent of these errors exists , the appropriate course is to perform an analysis of the sensitivity of the risk estimates to data errors . 3. Errors in Quantitative Modeling Several models have been developed in the preceding chapters, for es timating the distributions of such random variables as train speed , total number of cars derailing , probability that a train carries hazar dous materials, number of hazardous-material cars derailing , release probability , and amount released per car. Many of these models are based on historical data and involve a curve-fitting procedure which smoothes out fluctuations in the data. This smoothing procedure may be regarded as a logical method of correcting sampling errors in the data. On the other hand , differences between the fitted curve and the data may equally well be regarded as modeling errors. 122 4. Errors in Model Structure It is conceivable that some significant independent variable that alters risks has not been included in the analytical models. To the extent that the value of this variable in a future application of the models is different from its implicit value in the historical data on which the models are based , errors will occur in predicting risk. An example of such a hidden variable is a true measure of track quality. This report has used a surrogate for this variable; viz. , track class . It is known that the quality of track (and , conceivabl , the derailment y rate) may vary widely within a given track class. The models developed in this report are based on a nationwide averaging within each class of track. When applying these models , if the segments of track within a track class are sufficiently short, they may differ significantly in quality from the nationwide class average, and thus lead to errors in the risk estimates . Since errors of this type are forced by the lack of historical data on pertinent variables , there is no routine procedure for estimating their magnitude. In some instances, imaginative procedures can be developed , but they would involve substantial effort and have not, therefore , been pursued in this project . As an example, the nation 's track within a given track class could be segmented into several major groups--based on the owning railroad , for example. Accident rates can then be derived for each group, and statistical tests made to determine the significance of the differences , if any . c. REVIEW OF RISK-ESTIMATION PROCEDURE For convenience, the overall structure of the risk-estimation procedure is reviewed here. In the context of this discussion , "risk" is synonymous with "the probability distribution of the amount released." The first step is to determine the probability of a train accident , P , or the expected frequency of train accidents, m • The key histori A F cal variable is the accident rate, discussed in Section 3-G. 123 The second step is to determine the probability that the train carries hazardous materials, 0) , where PHis the number of PH = P(N > NH hazardous-material cars . H The third step is to determine the probability > 0 Accident P(. I and > 0) that the amount released is greater than ze�ro , given that NH a train carrying hazardous materials has been involved in an accident . The fourth step is to determine the probability distribution > 0) for the amount released , given that it is greater than p(zer�I�o . (Th e comb ined results of the second , third and fourth steps are presented in the tabulations in Chapter 10 .) The fifth and final step is to appropriately combine the four steps to develop an unconditional probability distribution for the amount released. In this context , it is important to no te that, in many situations , this distribution will have a significant mass , or probability, at 0; i.e. , the probability that no release occurs at � = all may be close to unity. The cumulative probability that a spill occurs will be small , and will be significantly altered by the probabi lity that no spill occurs . It is therefore possibly more important to es timate the errors in the probability that = 0 than in the distri � bution of given that it is greater than zero . �, D. QU&�TITATIVE ERROR ESTI��TES 1. Train Accident Rates Train derailment rates are estimated in Chapter. 3, Sect ion F, to have the following values per gross ton-mile: Class of Track I 2 3 4 5&6 Rate* per 53.2 17.3 5.59 0.589 0.840 Billion GTM * All causes . 124 There is no analytically correct and practicable procedure for esti mating bounds on these rates. An intuitively acceptable procedure has been devised and is recommended for use. For Class 3 track, as an example, the upper bound on the rate is taken to be the geometric mean of the rates for Classes 2 and 3 ; the lower bound is the geometric mean of the rates for Classes 3 and 4. For Class 1, the upper bound is taken to be: Rate Rate l l Rate x c: Rate x l Lower Bound l l Rate Rate ! I .; l 2 I 3 2 (Rate ) IRate = l / ... 2 Similarly, the lower bound for Class 4 is to be: Based on this procedure, the tabulation shown in Table 11-1 is arrived at . Because of the anomalous behavior of Classes 5 and 6, this procedure cannot be applied to them. Because of their relatively small level of exposure, it was no t considered important to develop bounds for their rates . It is also recommended that the same procedure be applied to track-caused derailments and to collisions . The results are as shown in Tables 11-2 and 11-3 . For yard accident rates , it is recommended that the bounds be derived by examining the bounding factors for Class 1 mainline accidents; the ratio of the upper bound to the best estimate and of the best estimate to the lower bound is 1.96 for derailments and 1.55 for collisions . If the same factors are used for yard accidents, the values shown in Table 11-4 are obtained . 125 TABLE 11-1. UPPER AND LOtolER BOUNDS FOR ACCIDENT RATES FOR VARIOUS CLASSES OF TRACK : ALL MAINLINE DERAILMENTS Class of Track 1 2 3 4 Lower-bound Rate * 30.3 9.83 1.82 0.191 Best Estimate Rate* 53.2 17 .3 5.59 0.589 Upper-bound Rate* 94 .5 30.3 9.83 1.82 * Per billion GTM . 126 TABLE 11-2. UPPER AND LOWER BOUND ESTIMATES FOR ACCIDENT RATES FOR VARIOUS CLASSES OF TRACK: TRACK CAUSED MAINLINE DERAILMENTS Class of Track 1 2 J 4 Lower-bound Rate* 16.9 4.24 0.624 0.056 Best Estimate Rate * 33.1 8.64 2.0S 0.187 Upper-bound Rat,e * 64.S 16.9 4.24 0.624 . * Per billion GTM. 127 TABLE 11-3 . UPPER AND LOWER BOUND ESTI��TES FOR ACCIDENTS FOR VARIOUS CLASSES O TRACK: MAINLINE COLLISIONS F Class of Track 1 2 3 4 Upper-bound Rate * 8.50 4.26 1.11 0.125 Best Estimate Rate* 13.2 5.47 3.32 0.372 Lower-bound Rate * 20.5 8.50 4.26 1.11 . 17 2 * Per 10 (gross-ton) miles . 128 TABLE 11-4 . UPPER AND LOWER BOUND ESTIMATES FOR ACCIDENT RATES IN YARDS: DERAIUIENTS AND COLLISIONS DUE TO ALL CAUSES Yard Derailments Yard Collisions Upper-bound Rate* 15.5 7.0 Best Estimate Rate * 7.9 4.5 Lower-bound Rate* 4.0 2.9 6 * Accidents per 10 cars . 129 2. Probability That Hazardous Materials are Present Given a train accident, the probability that hazardous materials are present on the train is PH. Historical estimate of PH are given in Table 5-3 ; a model for estimating PH in new situations is presented in Chapter 5, Section D. A parameter in that model is �H' the propor tion of hazardous-material cars to all cars. In the following the sensitivity of PH to variations in �H is examined, for the class of mainline derailments. For mainline derailments, historical data indicate that: �H = 0.018 (Table 5-1) and PH = 0.097 (Table 5-3) . Table 5-1 also indicates that within mainline track, �H varies from a low of 0.014 for Class 5 track to a high of 0.021 for Class 3 track. Using these as likely bounds on the value of �H for all mainline derailments, the formula in Chapter 5, Section 0 indicates that PH would vary from 0.076 to 0.119. This analysis. suggests that the following would be reasonable bounds for PH for mainline derailments: Uper bound = 0.097 x 1.2 = 0.116 = 0.097 1.2 0.081 . Lower bound = The factor of 1.2 is used to obtain symmetric bounds that closely approximate the observed bounds of 0.076 and 0.119, respectively. It is also recommendedtha t the same ratio of 1.2 be applied to obtain bounds on PH for other accident scenarios. 3. Probability of a Release The probability of a release, given a train accident, is: > 0) = & > 0) , P(Aa Accident) P x P(� > IAccident N I H O H the second termon the right being the conditional probability of a release, given that an accident occurs to a train carrying hazardous materials. Bounds on the factor PH have already been discussed. The conditional probability in the above expression depends principally on 130 two factors : the release probability q(v) and the number of hazardous material cars derailing , given a train accident . Uncertainties in the latter factor have been dealt tvith in the analytical model, tvhich is represented by both its mean and variance. The release probability , on the other hand , is presented only by its expectation. Reference to Figure 7-1 indicates that the regression actually used can vary significantly from the observed values. Typical errors are on the order of + 30% . If the estimates of q(v) are increased and decreased by these amounts for mainline derailments , one find s that > 0 Accident and N > 0) varies in direct proportion, ranging from P( I H a �low of 0.143 to a high of 0.265, with a best estimate of 0.204. (See Table 10-1 . For mainline derailments, the probability that = 0 � is 0.796 . The complement of this, 0.204, is the probability that > 0.) It is recommended that factors of 0.7 and 1.3 be appl ied to obAatain lower and upper bound s on O Accident and N 0) , for al l > H > accident scenarios . P(� I 4. Distribution of Amount Released, Given a Release The final step is to estimate errors in the conditional probability distribution : > 0) . p(�I� Fo r example , this cumulative distribution for mainline derailments may be derived as follows from Figu re 10-1: P(A x N > 0) - P(A = O N > 0 R � H R H = I 1 - O N > 0) = H P(� I A x N > 0) - 0.796 R � H = P( l 0.204 131 Thus , 0.054 l 0) 0.263 . � ooo > 0.204 P(� l� = = rigorous lower bound wa s developed for the cumulative distri A bution > 0) for all mainline derailments . methods of P(ARI� Two estima ting the upper bound were used , one based on estimating sampling error in the observed releases for wh ich the MTB data base provided data, and the second based on applying the Chebyshev inequality to th e observed distribution of the amount released, given a release. Th is inequality states that : The two bounds were developed for several values of x, and that � = one wa s used which was closer to the estimated distributions based on Figures 10-1 through 10-4. This is a 95 percent confidence level lower bound. The ra tio of the lower bound to the best estima te was then de termined, and applied in an inverse fashion to de termine an upper bound . The results are as shown in Table 11-5. As can be seen, the bounds are fairly tight, except at low values of x, where the importance of confidence bounds is diminished in any case . It is recommended that , for ease of application, a ratio of 1.1 or its inverse) be applied in all instances to obtain lower and upper ( on the bounds cumulative probability distribution � x � 0) . wn en this results in an ·upper bound on the probabilP(ity� largel�r than unity, the upper bound should be set equal to 1. 132 TABLE 11-5. UPPER AND LOWER BOUND ESTIMATES FOR THE CUMULATIVE DISTRIBUTION OF THE AMOUNT RELEASED PER ACCIDENT: ALL MAINLINE DERAILMENTS P 0) Amount (Aa � x l Aa > Released, Lower Best Upper Bound Estimate Bound Ratio x 1,000 0. 21 0.27 0.35 1.33 5,000 0.34 0.35 0.36 1.03 10,000 0.43 0.47 O.Sl 1.09 25,000 0.73 0.74 0.75 1.01 50, 000 0.83 0.95 1.00 1.14 100, 000 0.94 0.995 1.00 1.06 200 , 000 0.97 0.9999 1.00 1.03 133 12 • AREA AFFECTED BY A RELEASE A. INTRODUCTION The obj ec tive of this chapter is to develop an eas ily applied methodology for the probabilis tic estimation of the impact of hazardous ma terial releases upon th e public and its personal property , given the amount released in an acciden t, A • The techn iques used for es tima ting R the probability of a hazardous-material accident and the distribution of the amoun t released , given such an accident, are discussed in preced ing chapters . A guideline observed in developing the methodology was that it should be sufficiently general to permit impac t assessment for most categories of hazardous ma terials with minimal input from the user as to the specific charac teristics of the transport route and its environs . The development of a satisfactory methodology required considera tion of three cons traints: 1. The requirement that th e method allow rapid risk assessments of the transpor t of hazardous materials within entire regions of th e Un ited States, the implica tion being that one could not assume the ready availability of de tailed data for every segment of any particular route in order to perform a risk assessment. 2. The method had to address th e risks due to broad categories of hazardous materials , allowing the use of consolidated commodi ty flow data . Thus, the impact assessment method would have to incorporat e the average charac teris tics of those hazardous materials that comprise each of the several broad categories . 3. Since the specific environmental , topographical, and de�o graphic charac teristics of each route segmen t would not be ava ilable for use, and since hazardous materials were to be addressed in terms of broad categories, impact models for these categories should encompass only those maj or phenomena that characterize each ca tegory, i.e. , they cannot and should not attempt to model the unique features or haz.ards associated with specif ic ma terials within any given cate.gory . (This constraint logical ly follows from the first two .) 134 The outline of this chapter provides a convenient format for description of the approach that was developed . The sections of interest in sequence are entitled: • Selec tion of Hazardous-Material Categories, • Identification of Feasible Scenarios and Necessary Models, • Damage Criteria, • Selection of Representative Chemicals : Approaches to Impact As sessment, • Impact Assessmen t Hethods, and • Summary of Impact Assessment Results Although there ar e 35 categories of hazardous materials designated by four-digit Standard Transportation Commodity Codes (STCC) , the actual number of categories requiring detail ed consideration is far fewer . In the na�t section , the rationale for consolidating or deleting categories down to a total number of 12 is a� amined . Shipment s of explosives and radioactive materials were not included in the evaluation . Section B considers the three basic physical states of hazardous materials (compressed gases , liquids , and solids) and outlines their basic characteristics in terms of possible events upon their release. Section C iden tifies the generic assessment models needed to assess the hazards for any given release. Details of the models themselves are presented in Appendix C, while Appendix D describes how each is to be applied . Hazard-assessment models generally provide an estimate of the magn itude of a harmful physical parameter , such as the overpressure from an explosion, as a function of spatial coordinates and elapsed time . Section D--Damage Criteria--rev1ews the literature w1Lh the purpose of relating levels of such physical parame ters to exp ected effects on human beings and on proper ty . Ultimately , this allows estimation of the distance from the release site wi thin which people may expire, suffer 135 inj ury , or within wh ich buildings may be damaged. Thus , an impact assessment can be defined as the coupling of a hazard-assessment metho dolo gy with a methodology relating levels of damage to phys ical parameters . Section E presents the methodology for choos ing specific hazardous materials to represent each of the 12 categories. In addition , it describes how the results of impac t assessments for these materials were consolidated to provide estimates of the "average" and "wors t case" impac ts associated with each category. Mo st hazardous materials can cause more than one basic effect upon release. A liquefied compressed gas , for example, may vent as a gas and/or as a liquid. The gas may ignite to form a flame jet, travel downwind and ignite to produce a flash fire or detonation , or harm exposed people due to inhalation . Th e liquid may flash or form a pool , ignite to produce a pool fire, and so on . Section F--Impact As sessment �le thods--which covers conditional scenario probabilit ies, attem?ts to estimate the relative probabil ity of each maj or scenario feasible for each of the 12 categories of hazardous ma terials chosen previous ly . Section G--Surnmary of Impac t Assessment Resu1ts--provides the ac tual results of assessment model application to each of the repre sentative hazardous materials . For each feasible chain of events , it summarizes affected areas . and associated conditional probabilities of occurrence as a funct ion of the amount released , �. COMe.l[.va.u.ve M.6umptio� h.a.ve been ma.de .01 a. I1Wnb et'L o� .th e. .unpa.c..t M,� e6.6men.t modeU . ThU6 , we expec.t .thctt :the. me.thodolog en:ted y a.6 p'te,� give ovvz.u.t-Unctte 06 .the a.b.6 olute value 06 the .impa.c;t. Howevvz., �CUl a.I1 .the mode.U Me va.Ud 601[. ma.lU.ng c.ompCVt.Uon..6 be.tl.oeen ,UJ k-c.OYL:tJr.ol aUeltna,ti.vu, .tw bwtg .the. ma.jOil. objec..:U ve be.hbtd .the deveiopmen.t 06 .the M�e.6Jmen:t modelJ . 136 B. SELECTION OF HAZARDOUS-MATERIAL CATEGORIES 1. Background Commodity flow data for hazardous materials are recorded in accordance with the Standard Transportation Commodity Code (STCC) classification scheme . At the four-digit level , these codes designate' 35 individual categories , many of which are quite similar to others in chemical and physical attributes . An an alysis of the behavior of hazardous materials upon their release and of the various mechanisms by which the public or its property can be adversely aff ected reveals that there are far fewer such mechanisms than there are STCe categories . Indeed, one can only envision the following actions of hazardous materials involved in a typical railroad accident : • The hazardous material remains in the container; • Gas vents from the tank; • Liquid vents from the tank; • Spilled liquid has a low vapor pressure--it does not evaporate; • Spilled liquid rapidly vaporizes (due to boil ing) ; • Spilled liquid slowly volatilizes; and • The solid spills and remains upon the ground. Depending upon whether the hazardous material is ignited or no�, the only significant damage mechanisms are the following: • Fires or burns due to thermal radiation exposure after gas, vapor , liquid, or solid ignition ; • Injury or damage due to the effects of an explosion; • Injury due to toxic vapor or gas inhalation; • Inj ury or damage due to direct contact with the hazardous material; 137 • Injury or damage due to contac t with , or inhalation of , radioactive materials ; and • Inj ury due to rocketing of car fragments . The difference between the number of four-digit STCC categories and the number of post-release phenomena suggests that an attempt to conso lidate the 35 STCC categories into a more managab le and pertinent set is warranted . This is accompl ished below through a systematic evalua tion of each category, elimination of tho se that are not des ired or cannot be addressed by the current study , and consolidation of those which are differentiated by attribu tes not pertinent to the task of impact assessment. 2. Class A, B, and C Explosives Comprehensive commodity flow data for explosives are generally unavailab le to the Department of Transpor tation , since most such materials are shipped under the direc tion of the Depar tment of Defense. Consequently , the hazardous materials comprising the three STCC cate gories for explosives are not addressed in this study . 3. Compr essed Gases The category of non-flammab le compressed gases includes a wide variety of compressed gases, either liquefied or non-liquefied, 'that do not meet the flammability criteria set forth in 49CFR l73 .300(b) . Within this group are those materials wh ich may be oxidizing , cryogenic, po is onous or corrosive, or possess combinations of these attributes, as we ll as those that may be simp le asphyxiants . Similarly, the maj or category of flammable compressed gases includes sub stances that are pyropho ric (which is rare) , oxidizing , poisonous , corrosive, or even detonable under the proper cond itions , as well again as those which are simple asphyxiants if not ignited. Because of the rather unique properties and hazards of the materials in these categories , it is prudent to retain the individual classif ica tions , "Non-flammable Compressed Gas" and "Flammable Compressed Gas ," in subsequen t analyses . 138 4. Flammab le Liquids The five STCC categories encompassing flammable liquids include all materials that are liquids at amb ient pressures and temperatures and wh ich have flash points below 100°F (37. 8°C) . Hembers of subgroups may also be pyrophoric , thermally unstable, poisonous, polymerizable, or corrosive . All of these materials have the basic attributes of being relatively vo latile liquids with a high fire hazard and the potential for toxic vapor exposure or inj ury by direct contact. Consequently, the five individual categories can reasonably be consolidated into the single category of "Flammable Liquids ." 5. Combustible Liquids Three STCC categories exist for liquids with flash points at or ab ove lOOoF (37. 8°C) and below 200 °F (93. 3°C) . With generally lower vapor pressures , the hazardous materials covered are not so hazardous as flammable liquids. Nevertheless, under appropriate conditions , tho se with flash points near the lower end of the given range can produce the maj or impact scenarios associated with flammable liquids . It is feasible to cons ider all such materials under the single category of "Combustible Liquids ." 6. Flammable Solids According to 49 CFR 173.150, a "flammable solid is any solid material , other than one classed as an explosive, which, under conditions normally incident to transportation, is liable to cause fires through friction, retained heat from manufacturing or processing, or which can be ignited readily , and , when ignited, burns so vigorously and persis tently as to create a serious transportation hazard. Included in this class are spon taneously combus tible and water-reactive materials." Such sub stances are covered by two STCC categories including such diverse ma terials as oily rags, fish scraps , phosphorus , and metallic sodium. 139 The first four-digit STee category (49 16) for these hazardous materials includes mainly specific chemical or metallic materials (such as phosphorus , metallic sodium, powdered magnesium, and the like) which have an unusual hazard potential . Thus, it is recommended that this category be retained as a separate en tity. Th e second category cons ist ing mainly of ordinary combustibles such as rubber scrap , oily rags, fish scrap, and ground charcoal, must ther efore also be kept separate. To differentiate between them , the first will be referred to as "Flammab le Solids--Special Hazard" and the second as "Flammable Solids- Ordinary Hazard ." 7. Oxidiz ing Haterials An oxidizer is a substance that readily yields oxygen to stimulate the combus tion of organiC matter. The single STCC number for this category covers liquids , such as fuming nitric acid as well as numerous solids . Since a single STCC number is pr ovided and solids are not classified separately from liquids, th e single category of "Oxidizing Materials" is appropriate for further analyses. 8. Organic Peroxides With certain qualifica tions, an organic peroxide is generally a derivative of hydrogen peroxide in which one or more of the hydrogen atoms has been replaced by organic radicals . Relatively few in numb er , the subs tanc es covered by this category include bo th so lids and liquids and can be addressed as a single category. 9. Poison Class A and Poison Class B Class A pOisons are gases or li�uids of such a nature that a very small amount of the gas or vapor of the liquid when mixed with air becomes dangerous to life. Class B po isons are liquids or solids, other than Class A po isons or irritating ma terials , which are known to be so toxic to man as to create a hazard to health during transportation; or which, in the absence of adequate data on human toxicity, are presumed to be toxic to man because they fall within any one of the three specified 140 toxicity categories when tested on laboratory animals . Th e various sub stances designated as Class A or B pOisons may also be flammable, ox idizing, or co rrosive. Since "Class A" refers to gases and liquids , and since these physical states, on average, disperse more widely than the states associated with Class B poisons, it is necessary to retain each class as a separate entity. These will be referred to by the terms "Poison Class A" and "Po ison Class B." 10. Irritating Ma terials and Etiologic Agents An irritating material is a liquid or solid substance, not including any Class A poisonous material , that , upon contac t with fire or when exposed to air, gives off dangerous or intensely irritating fumes . An etiologic agent is a viable micro-organism, or its toxin , which causes or may cause human disease. Since there is a single category for these materials, and they have some unique properties , the category is retained with the designation "Irritating Haterials." 11 . Radioactive Haterials Because of the special nature of radioactive ma terials and the considerable complexity and difficulty in assessing the impac t of releases to the environmen t, it was decided that these hazardous materials would not be addressed in this study. 12 . Corrosive Materials A corrosive material is a liquid or solid that causes visible destruction or irreversible alterations in human skin tissue at the site of contact, or , in the case of leakage from its packaging, a liquid that exhibits a severe corrosion rate on steel . Within the seven four-digit STCC categories devoted to this category are included substances which ar e additionally poisonous , or in the unique case of bromine, al so oxidizing. 141 The nature of the seven STCC ca tegories does not allow or warrant their differentiation in subsequent aspec ts of this analysis . Conse quently, all seven categories can be consolidated into the single ca tegory of "Corrosive Materials ." 13 . Other Restricted Articles : Groups A, B, and C These three STCC categories--Groups A, B, and C--are a "catchall," for materials that do not meet any definition of a hazardous material per se, but which nevertheless have certain undesirable properties . Since the materials cannot be considered significantly hazardous and may have vastly dissimilar properties, they are not included in the subse quent analysis . 14 . Summary Table 12-1 presents a summary of the categories remaining af ter consolidation or deletion of the 3S individual classif ications origL�ally considered . In addition, it notes the four-digit STCC numb ers covered by each ca tegory . Table 12-2 is a compilation of data from the Material Transportation Bureau from 1971 through 1977 . These data ind ic ate that the 12 cate gories in Table 12-1 cover 100% of all deaths due to hazardous-material release , 98% of all injur ies , and 99% of all releases . It is apFarent that the deletion of certain STCC categories does not significantly alter the coverage of the types of impact of greatest concern . C. IDENTIFICATION OF FEASIBLE SCENARIOS AND NECESSARY MODELS 1. Background The task of impact mod eling requires the identification of analy tical techniques for estimating the area that will be affected by a hazardous-material release . This effort, in turn , requires identifi cation of those phenomena which are capable of causing death, inj ury , or pr operty damage upon release of the hazardous ma terial . 142 TAB LE 12-1. SUMMARY OF SELECTED HAZARDOUS-MATERIAL CATEGORIES Category STCC Numbers l. Non-flammable compressed gases 4904 2. Flammable compressed gases 4905 3. Flammable liquids 4906, 4907, 4908 , 4909, 4910 4. Combustible liquids 4912 , 4913, 4915 5. Flammable solids : special hazard 4916 6. Flammable solid : ordinary hazard 4917 7. Oxidizing materials 4918 8. Organic peroxides 4919 9. Poison Class A 4920 10 . Poison Class B 4921, 4923 1I . Irritating materials 4925 12 . Corrosives 4930 through 4936 Note: STCC numbers deleted from consideration include: 4901-4903 for explosives , 4926-4929 for radioactive substances, and 4940 , 4943 and 4946 for "other restricted ar ticles ." 143 TABLE 12-2 . RELATIVE COMPARISON OF HAZARDOUS-MATERIAL GROUPS BY SEVERITY MEASURE* Number Number Number of Commodity Killed Inj ured Releases Explosives 0 60 42 Non-flammable 2 450 378 compressed gas Flammable compressed 14 345 562 gas Flammable liquid 1 275 1043 Flammable solid 2 85 86 Oxidizer 0 30 325 Organic peroxide 0 5 1 Toxic 0 125 190 Radioactive 0 0 6 Corrosive 0 1555 1749 Miscellaneous -0 0 --6 Total 18 2930 4388 *Based on data from Materials Transportation Bureau for 1971-1977. 144 2. Release Scenarios It is best to discuss release phenomena in the context of the physical and chemical properties of substances . Therefore, the basic ca tegories of gases, liquids, and solids are investigated in the follow ing subsections to identify phenomena of interest for subsequent modeling efforts. a. Compressed or Liquefied Gases Figure 12-1 shows an event tree for the events that are most likely to occur wh en a tank car of compressed or liquefied gas is involved in a railroad accident. Starting from the accident itself at the top of the diagram, rectangles identify the discrete series of events that may follow. For massive releases of gas or flashed vapors , it is evident that a vapor dispersion model is necessary ; one preferably designed for instantaneous releases to the atmosphere. It is also clear that : • The model must allow estimation of the size of the hazard zone in the event that the cloud ignites to cause a flash fire or a free-air detonation ; • Some method is needed to es timate the probability of cloud ignition as a function of time; and • An approach is desirable for estimating the amount of vented liquid that immediately flashes to vapor . �ediate ignition of venting gas requir es a flame-j et model, whereas ignition of spilled liquid necessitates a model for pool fires. Slow evaporation of a liquid after supercooling and pooling sugges t the need for a teChnique for estimating the rate of an evaporation, as well as a continuous-source vapor-dispersion model . Finally, the possibility that the tank car may experience a boiling li quid expanding vapor explosion (BLE VE) , or otherwise explode, requires yet another method for hazard-zone estimation . 145 Release Flashes Liquid Vapor Cloud Travels Downwind Vapor Cloud IgnillH - Detonalion Occurs Vapor Cloud Ignites - F luh ire Occurs F No Ignition-ToKic Vapor Exposure Pool Fire Occurs FIGURE EVENT TREE FOR COMPRESSED GASES 12-1. 146 Scenarios not addressed by the event tree include spills of soluble liquids in to water and the subsequent use of that water for public consumption or crop irrigation . In addition , no consideration is given to any harmful effects of such spills upon aquatic wildlife. b. Liquids If liquid spills into water are ignored , scenarios of interest will be those shown in the event tree of Figure 12-2 . These scenarios are a subset of those presented for compressed gases, and any models provided for liquefied gases should be adaptable to these liquids of lower volatility. c. Solids Formulation of an event tree for releases of solids is not necessary because these rarely cause maj or inj ury or damage. Two models suffice: one for the burning of ordinary combustibles, and another for the burning of substances with special hazards . d. Summary Based upon the results of the previous analysis, it is possible to develop a model "f1owsheet" that designates the required models and shows how the o�tput of some models satisfies the input requirements of others. Figure 12-3 presents such a flowsheet; the capital letters A through M are used to indicate individual models . 3. Details of Models Appendix C provides details of each of the hazard models utilized in the study. Appendix D describes how the models were applied for the purposes of impact assessment. D. DAMAGE CRITERIA 1., Bac kground Hazard-assessment models permit users to es timate the concentration levels of toxic and physical agents at specified locations and times 147 Accident I Tankcar ExplO$ion No Releasefr------+------�l or BLEVE No Impact Release I 1 1 Low Vapor Pressure High Vapor Preuure Liquid Liquid Pool Slowly I No Ignition Evaporates , PoOl Fire I Occurs Poo l Fire l Occurs Vapor Plumo Travels Downwind Plume Ignites: FlashbOlcl( Occurs No Ignition.Toxic Vapor Exposure Pool Fire Occurs IDS EVENT TREE FOR LIQU FIGURE 12-2 .. 148 Reluse F Tankc:ar Explosion l Fire Model Special Hazards liquid Flilsh B MOIM M " K Iqnilion Liquid Pool Fire Modlll Fire Model Ordinary Hazards Mod�1 c InSlilnl.. neous Source I-' Vapor Dispersion Model � \0 A Ignilion Conlinuous Vilpor Sour" Model Dispersion Model D flash Fire Model E DO:lonallon Model FIGURE MODEL UTILIZATION FLOWSHEET 12-3. after a spill . For overall risk-assessment purposes, however, their results must be translated into estimates of the harm to members of the public and their property . 2. Explosion Effects Appendix D of Ref . [1] notes the necessity of relying upon the results of studies conduc ted for and by the Military in assessing damage caused by explosions . Al though such studies have concentrated upon investigations of condensed-phase and nuclear explosions , as opposed to the diffuse explosions more typically expected from the release of hazardous materials, results stated in terms of basic blas t wave para meters (overpressure, for example) can be considered suf ficiently accurate for universal application. In documentation cited above [1] , prepared for the U.S. Coast Guard during its vulnerability modeling program, the available damage-assess ment techniques are reviewed and expressions direc tly applicable to the current study are derived . These are pr esented in the following sub sections along with discussions as to how they should be utilized. a. Classification of Effects on Humans Numerous documents and studies have classified damage to p�ople caused by explosions into three categories : 1. Primary Damage--Direct blast effects caused by the interaction between the blast wave and personnel only , with no other intervening factors; 2 . Secondary Damage--Injury due to missiles and fragments; and 3 . Tertiary Damage--Injury due to translation (violent movement due to the blast wave) and subsequent collision with an obstacle. b. Primary Damage Referen�e [1] utilizes da ta from Ref . [2] to relate the peak over pressure from an explosion to lung hemorrhage, the primary cause of death from direc t blas t effects . Us ing the free-field (side-on) over- 150 pressure at infinitely large durations in assessing levels of lethality (current practice) , one can develop an expression in the form: = -77 .1 + 6.91 Log (P ), (12-1) Pr e p 2 where P is the peak overpressure at any location in units of N/m, and p p is a measure of the percent of the vulnerable resource affected in r the form of a normally distributed random var iable with a mean value of 5 and a va rianc e of 1. Given a value for p , a user would en ter r Table 12-3 to read the percentage of exposed people expec ted to be 2 killed . For example, an overpressure of 150,000 N/m ins er ted in the equation gives a p value of 5.26. Enter ing Tab le 12-3 with this value r then suggests that approximately 60% of humans (and probably other animals) would die from exposure to the stated overpressure. The main non-lethal inj ury expec ted from direc t blast effects is eardrum rupture. Again , wi th data from Ref . [2] , Ref . [1] derives the equation : = -15 .6 1.93 Log (P ). (12-2) + e p 2 For the same overpressure of 150,000 N/m, p now has a value of 7.4, r and thus approximately 99.2% of the exposed popUlation could be exp ec ted to be affec ted . c. Secondary Damage The task of developing similar expressions for secondary damage due to explosions (injury due to missiles , fragments, and environmental debris set in mot ion by the event) is considerably more complex. It is difficult to assess the size distribution and detailed motion of thousands of individual missil es , or estimate the probability of impact with exposed humans . As an approximation , Ref. [1] presents the expression : = -27 .1 + 4.26 Log J, e (12-3) 151 TABLE 12-3 . RELATIONSHIP BETWEEN PERCENTAGES AND p'S r % 0 1 2 3 4 5 6 7 8 9 0 - 2.67 2.95 3.12 3.25 3. 36 3.45 3 .52 3.59 3.66 10 3. 72 3 .77 3.82 3.87 3. 92 3.96 4.01 4.05 4.08 4.12 20 4.16 4.19 4. 23 4.26 4.29 4.33 4.36 4. 39 4.42 4.45 30 4.48 4.50 4.53 4.56 4.59 4.61 4.64 4.67 4.69 4. 72 40 4. 75 4. 77 4. 80 4 .82 4.85 4.87 4. 90 4.92 4.95 4.97 50 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5. 18 5.20 5. 23 60 5.25 5.28 5.31 5.33 5.36 5. 39 5.41 5.44 5.47 5. 50 70 5.52 5.55 5.58 5.61 5.64 5.67 5. 71 5.74 5.77 5.81 80 5.84 5.88 5.92 5.95 5. 99 6.04 6.08 6. 13 6.18 6. 23 90 6.28 6.34 6.41 6.48 6.55 6.64 6. 75 6.88 7.05 7. 33 - 0.0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0.8 0. 9 99 7.33 7.37 7.41 7.46 7.51 7.58 7.65 7.75 7.88 8.09 The p values are the three-digit numbers in the table . Percents are readr along the top and side margin of the table. The vertical co lumn of percents gives the decade ; the ho rizontal co lumn gives th e unit. The table en try appearing in the row of the decade value and the column of the unit value is the p value corresponding to that percent. The last two rows in the t ble provide a finer reading fo r very high percen t--from 99 .0 Ato 99 .9. The second to last row is the tenths of percent to be added to 99% . The last consists of the corresponding values. row p r 152 where J is the dynamic overpressure impulse def ined by the integral of the overpressure as a function of time for the duration of the positive 2 phase of the blast wave (in units of N-s/m ). In mathematical terms : t o J peT) dT. (12-4) = f t a where peT) = overpressure as a func tion of time at a given location , t arrival time of the blast wave, and a = t time at which positive phase of the blast wave ends . o = Deriva tion of this expression for P assumes that all exposed persons r ou tside of buildings in the region traversed by the blast wave would suffer injury from missiles . Th is assumption leads to overestimates of the expected injury rate. In the absence of a more rigorous approach to the problem, however , it must be utilized until better criteria become available . d. Tertiary Damage Reference [11 deals with deaths and inj uries due to forcible movement of exposed people and subsequent impact with the ground , a wall, or other obj ec t due to the blast wave . Assuming an average sized person and an impact distance of 10 feet, one can derive the following expression: = -46 .1 4.82 Log J, (12-5) + e 2 where J is the impulse level in N-s/m and leads to the percentage pr of exposed popula tion killed . For injury, mostly broken bones , the expression presented is : -39.1 4.45 Log J. (12-6) = + e 153 Evaluation of these expressions indicates that damage due to impulse is completely overshadowed by damage due to overpressure at any point, and it is reasonable to ignore the former . e. Explosion Damage to Structure Using data from Ref . [2] for frame structures exposed to the blas t wave caused by 500 tons of TNT (based on Ref . [1]), one can derive the following two a� pressions : • For glass breakage only : = -18 .1 2.79 Log and (12-7) + e (pp ); • For structural damage: = -23 .8 2.92 Log (12-8) + e (pp ); where P again is the peak overpres sure at a given location in units of p 2 N/m. Reference [2] repor ts that threshold glass breakage (1%) occurs at 2 a peak overpressure of 1,700 N/m . By as suming that 90% of all glass 2 will break at the overpressure level (6, 200 N/m ) associated with thres- hold structural damage (1%) , Re f . [1] obtain s the two data points needed to derive the p expression. Th e approach appears to be conservative, r but logically correct in a qualitat ive sense. It ultimately provides the percentage of buildings that will experienc e glass breakage as a function of overpressure. The approach for es timating the percentage of buildings that will suffer structural damag e is not so logically correct, however. Reference (2) provides data relating the extent of damage to a given frame building as a funct ion of overpressure. Th ese data are: 2 Damage Level Peak Overpressure (N/m ) Threshold structure damage (1%) 6,200 Structural damage (50%) 20, 700 Total damage (99%) 34, 500 154 It appears that Re f. [1] incorrectly assumes that 1% of buildings will 2 2 experience damage at 6,200 N/m , 50% will suf fer damage at 20, 700 N/m 2 and so on , where in truth the 20,700 N/m overpressure is intended to sugges t that 50% of a given building is destroyed . This interpretation is confirmed by data in Ref . [3] , indicating that an overpressure of . 2 . 20,700 N/m is sufficient to shatter non-reinforced concrete or cinder block walls , and that entire walls of standard type homes can be blown 2 in at the lower overpressure of 13 , 800 N/m • To resolve this inconsistency in Ref . [1] , it is concluded that the second p expression presented above can only be utilized to assess r the level of damage to a structure exposed to a given overpressure. Furthermore, it is concluded that shielding effects in densely populated areas , at some later time , should be given credit, so that the second or third line of structures around a blast site are not assumed to suffer the same damage levels as structures in the first line or ring about the site. f. Additional Considera tions Reference [1] has not attempted to es timate the numb er of deaths and serious inj uries to persons inside buildings that suf fer sub stant ial damage . Obviously , if a building suffers total destruc tion because of a blast, people inside that structure will be hurt. As a first attempt at deriving P expressions for these cases, it r is suggested that 50% of people in a building that suffers total damage will die and that 90% will be injured signif ican tly . If the structure is 50% damaged, it is suggested that 25% of the inhabitants will die and that 12 .5% will be injured . These es timates allow this factor to be addressed quantitatively. Thus; • for deaths due to building damage: P = -8 .7 1.31 Log and (12-9) r + e (P p ); 155 • for injuries due to building damage : = -4 3.51 4.77 Log (P ). (12-10) + e p 3. Fire Effects An assessmen t of the impac t caused by a vapor-cloud flash fire or a burning pool requires consideration of thermal radiation levels as well as the duration of exposure. Using data from Ref . [4] , one can use Ref . [1] to derive the following expression for death from burns : 4/3 -4 = -14 .9 2.56 Log (tl x 10 ), (12-11) + e where t is the duration of exposure in seconds and I is the thermal 2 radiation flux in jou1es/m -s . For non-lethal burns, it is desired to obtain an expression describing the threshold for first-degree burns . Reference [1] finds that the equation described by: = 550, 000 (12-12) fits the data well. If exposures in any region exceed this level, non lethal burns can be exp ected for exposed personnel. Where property is of concern , levels at which exposed wood ignit�s spontaneously have to be evaluated. Reference [1] develops the necessary criteria through man ipulation of an analys is pres ent ed in Ref . [5] . For ignition of wo od from pool fires , the radiation in tensity (I ) must exceed the level: s 4 2 I = 2.54 x 10 jou1eslm -s , (12-13 ) s and the duration of the fire mus t exceed the time given by: 1.25 t ; (61 , 000/1 - I ) (12-14) r s 156 4. Toxic Effects As a practical matter , the release of toxic substance to the environment cannot generally be exp ec ted to affect large exposed populations adversely, unless the substance disperses rapidly and in such a manner as to afford no chance of escape to affected people. Thus , an assessment of potentially widespread and significant toxic effects can be limited to a consideration of harmful acute exposures deriving from vapor inhalation . Chronic (i.e. , long-term) exposures to harmful vapor conc entrations can be excluded on the basis that the public will voluntarily and promptly evacuate potentially harmful areas , or will be forced to do so by public health offic ials . Similarly, the likelihood of ingestion and or skin or eye contact with hazardous substances in the solid or liquid state can be considered a rare event except under extraordinary circumstances . Although a few foolhardy members of the public may wander through a spill site, and a few careless or uninformed memb ers of emergency response forces may be affected , their numbers will generally be few and not of consequence to the final result of an overall, comparative risk assessment . An assessment of the effects of a toxic vapor cloud necessitates the classification of exposure consequence into three categories : • Lethal injury, • Sublethal inj ury, and • Severe irritation . Lethal injuries (or fatalities) will occur at vapor concentrations sufficiently high to cause death immediat ely , or within a time span less than that necessary for escape to less affected regions . To simplify the selection of lethal exposure levels for representative hazardous substanc es , it is not unreasonable to assume that the maximum available time for escape from a hazardous condition is one-half hour . The lethal concentrations associated with this time dur ation then provide the desired criterion for estimating the area in which the exposed population 157 may expire. The selection of such a simple criterion obviates the need for complex dose-response relationships , while providing a conservative approach to satisfying the needs of impact analysis . During the joint National Institute of Occupational Safety and Heal th! Occupational Safety and Health Administration (NIOSH!OSHA) Standards Completion Program, considerable effort was devoted to the definition of concentrations that are "immed iately dangerous to life or death." The resulting Immediately Dangerous to Life and Health (IDLH) levels for OSHA regulated substances [6] were chosen to represent the maximum concen trations from wh ich a person could escape within 30 minutes without any escape-impairing symptoms or any irreversible health ef fects. These concentrations , therefore, provide convenient and generally realistic values for use in def ining the borderline between concentrations that are harmful and those that are severely irritating . Memb ers of the public experiencing moderate to severe irritation are likely to be concerned that their exposures have caused them more serious harm. In consequence, they may seek medical treatment and add to the burden of emergency medical teams . It is worthwhile, therefore , to develop a conservative definition of concentration levels that are capab le of caus ing significan t irritation. Table 12-4 lists representative chemicals * that can cause va·por exposures over widespread areas . For each of these chemicals, the table provides es timates of each of the three conc entration levels described ab ove , based upon a review of the pertinen t literature. 5. Application of Damage Criteria The vapor concentrations presented above are well suited to the estima tion of affected downwind areas . The other damage criteria , however , are in the form of equations relating a physical parameter to the frac tion of exposed resources that are expected to be harmed . They are better suited, therefore, to more rigorous risk assessments, which are beyond the obj ectives of this study. * These hazardous ma terials were selected through a process describ ed in Sec tion F. 158 TABLE 12-l:. . TOXIC VAPOR OM-IAGE CRITERIA FOR THIRTY MINUTE EXPOSURE Lethal Sublethal Irritating Chemical (ppm)** (ppm) (ppm) Ammonia 2500 500 14 0 Aniline 500 100 0 Boron Trichloride 3000 100 75 Bromine 400 10 2 Chlorine 50 25 7 Oimethy1amine 4000 2000 300 Gas oline 8000 2000 1000 Hydrochloric acid 4350 100 50 Hydrogen chloride 3500 100 75 Hydrogen sulfide 600 300 240 Me thyl alcohol 70000 25000 0 Me thy1 bromide 2600 2000 1500 Nit robenzene 1000 200 0 Nitrogen tetroxide 800 SO 20 Phosgene 15 2 1 Sulfuric acid 75 20 2 Toluene 10000 2000 1500 Xy lene 15000 10000 4000 Butadiene .. Ethylene Hydrogen 600000 450000 300000 LPG Monoch1orodif1uoromethane J * Th e vast maj ority of these criteria evolved from a rapid review of limited available data from experiments with animals and the application of a considerable degree of judgment . It is en tirely possible and likely that one or more values are sub stant ially incorrect. ** ppm � parts per million. 159 To simplify applications of these la tter criteria , it was decided to utilize the equations to define the physical parameter values asso ciated with a 40% probability of damag e . Furthermore, it was assumed that the deaths , inj uries , and property losses expected from a parti cular release scenario could be derived by totaling only those losses occurring within the 40% damage isopleth , this being accomplished by further assuming that all resources within th e hazard area have the pot ential to be adversely affected . In this approach, overestimation of damages within the 40% isopleth will hopefully be counterbalanced by the assumption tha t no damages occur outside . Table 12-5 summarizes the damage criteria for explosions and fires using this strategy and others noted on the table for special cases . E. SELECTION OF RE PRES ENTATIVE CHEMICALS : APPROACHES TO IMPACT ASSESSMENT 1. Background It is th e obj ec tive of this portion of the analysis to review historical hazardous-ma terial spill statistics to identify those subs tances that have been mo st commonly spilled . Th e short list of substances developed for each ca tegory is subsequently utilized to develop impact assessmen ts for both "average" and "worst case" spill scenarios. The approach for this effort is also described in the following paragraphs , while the results are presented in Section G. 2. Data Sources Utilized Ideally, the data base for spills would only include those incidents involving railroad cars . Unfor tunat ely , however, the task of sorting and analyzing existing data bases to obtain such data wo uld have required a massive and costly effort that wa s not considered as being justified by the obj ectives of this study . Thus , the analysis of spill data considered all spills reported to the Department of Transportation (DOT) as being transportation-related . 160 12-5 . SUMNARY PIIYS ICAL AGENT IlANAGE APPLICATION CRITERIA TAB LE 010' ANI) Basic Damage Damag ng i Event Re epto s Effect Cause c r Fa ctor Dama2e Ci'lteria Criteria Bases Applic;ltton 2 E plos on lIumans eth l Lung Peak 1 39,407 H/m 40% Lethali ty Outdoor Population x i L a Injury Hemorrhage Overpressure 2 lIumans Non- lethal Eardrum Peak 37,9U Him 40% Injury Outdoor Population InJ ury RUl'ture Ove rl'reS8Ure 2 Humans Non-lethal tlisslles Dynam ic 1,766 N-s/m 40% Injury Outdoor Populat ion Injury Overpressure Impulse 2 3 Ifumans Lethal Du Uding Peak 28 ,77 Nlm 40% Lethality Indoor Population Inj ury C01 la,>lIe Ovcqlressure ! 2 lIumans Non- lethal Build ing I'cak 24 . 770 Nlm 40% Injury Indoor Population Injury C:ollallse Overpressllre I-" 0\ 2 I-" Bui ldings Glass Shock Wave I'oak 3 ,605 N/m 40% Available Structures Breakage OVerl)resSUre Glass Breakage 2 Bu ld n s Strllctural Shock 17 ,631 40% Structural Structures i i g I�ave I'(!nl( N/ru DlImage Overl·rcssure Damage l 33 7 Fire an Lethal Burns The rmal tl • _ 2.16xl0 2 40% Lethality Ou tdoor Population Hum s J/m (any In ury at o j Rad i i n type) • 5 5 2 lIuPlans Non- tha Burns t _ 5.5xl0 /m Love r Limit Outdoor Population ll! l 1'hcTlllal I l 1 J Injury Rud lllLion 4 2 Pool Bui d n s Fire I nit on 'h r l I 2.54xlO Jim -s and Lowe r Limi t St ructure l I g g I 1 e ma r > s Fire Damage Rad iation 1.25 61000 t ;. - [ - I r 1 s J Notes: t durat ion of fire exposure (seconds) ef fective 2 effect d a n int�ns ity at rl!ceptor (Jim -s) 1 r ive4 ra i tio I .. 2.54xl0 s J/m2-s In 19 77, the DOT Office of Hazardous Haterials (OHM) made ava ilable a detailed an alysis of the 12,063 hazardous -material inciden t reports received during calendar year 1976. Encompassing all modes of trans por tation , but primarily consisting of reports from highway and railroad carriers, the detail ed data sh ee ts lis ted al l substances spilled in that year , identified the commodity category of each , and provided the exact number of spills involving each substance. It wa s decided to utilize the results of this effort to identify the hazardous materials to be used in developing the "average" and "worst case" impact-assessment scenarios . Necessary assumptions are: That the mix of commodities that are trans ported by • . railroads and that ar e involved in accidents does not vary substantially from the distribution suggested by the OHM data ; and • That the results of the impact as sessment would not be significantly distorted by the inclusion of a few "erroneous" substances in the list (vis-a-vis shipment by railroad) , if some judgment is applied to adj ust results. 3. Approach Th e analysis for non-flammable compr essed gases present ed below demonstrates the overall approach taken to developing a short list of substances that presents the bulk of the risk associated with spills of this type of substance. For this particular category , the effort ultimately led to a lis t of six spec ific sub stances (one is actually representa tive of the broader class of simple asphyxiants) that have been most often spill ed in the past . Each substance is assigned a conditional probability of release, given that an accident has occurred and that a substance in this commodity category has been rel eased. A sub sequent portion of the overall impact-assessment analysis evaluates the areas associated wi th th e maj or adverse effects of each substance as � function of the amount released. Analogous areas for each substance (e. g., the areas in which humans will expire due to toxic vapor exposure) are then utilized , in combination with conditional 162 probabilities , to develop "composite" results that are representative of the effec ts of th e average or typical spill involving this category of ma terials . A simple inspection of overall results then permits selection of those results associated with feasible "worst case" events . With these two sets of data, the analyst can consider wha t is most likely to occur during a typical incident, and also define th e upper limits of expected adverse impacts . 4. Analysis for Non-flammable Compressed Gases The maj or impac t of a non-flammable compressed gas (NFCG) release is exposure of the public to airborne contaminants. Tab le 12-6 presents a summary of th e NFCG releases that occurred during 1976 and lists the concentrations in air that are immediately dangerous to life and health (i. e. , IDLH values extracted from OSHA documents cited previously or estimated by Ar thur D. Little) . Where the word "asphyxiant" appears in this list, it implies that the gas or vapor is not truly toxic, but can nevertheless cause harm through depletion of oxygen in the atmosphere. All such designations were made by Arthur D. Little, based upon a review of toxicological data . Substances with IDLH ' s of 50 ,000 ppm can also be considered simple asphyxiants for th e purposes of this analysis , although it must be realized that some of the sub stances with this IDLH do have additional toxicological effects. Table 12-7 separately combines all simple asphyxiants and all commodities with not otherwise specified (NOS) designations , and, in its second column , presents the fraction of all spills associated with each specific commodity or type of commodity. These results are essentially the conditional probab ilities of release . They are not useful as yet, however, because the category of NOS materials is comprised of materials with undefinabl e properties . Thus , it is assumed that the NOS materials are distributed in terms of adverse impact in a fashion similar to the better identified commodities, and "adj usted" conditional probabilities of release are computed with simple ratios. These ar e presented in the third column of the table. 163 TABLE 12-6. NON-FLAMMABLE COMPRESSED GAS SPILL DATA (1976) Conunodity Number of IDLH Releases (ppm) Anhydrous ammonia 80 500 Argon 1 Asphyxiant Bo ron trifluoride 2 100 Chlorine 11 25 Compressed gas (NOS) 40 ?. Carbon dioxide 9 50 ,000 Dichlorodifluoromethane 3 50,000 Dispersant gas (NOS) 1 ? Fe rt . ammoniating sol . 2 ? Fire extinguishers 6 50 ,000 (est .) He lium 1 Asphyxiant Hy drogen Chloride 5 100 �Ionoch10 rodif 1uo romethane 1 50 ,000 (est .) �itrogen fertilizer soluble 3 ? Nitrogen 3 Asphyxiant Oxygen 6 164 TABLE 12-7. DATA ANALYSIS RESULTS FOR NON-FLANMABLE COMPRESSED GASES Commodity P P(adj usted) Anhydrous ammonia 0. 461 0.656 Asphyxiants 0.138 0.197 Chlorine 0.063 0.090 NOS compounds 0.264 - Hydrogen chloride 0.029 0.041 Boron trichloride 0.011 0.016 Oxygen 0.034 - 1.000 1.000 Note : Monoch10rodif1uorome thane is chosen as representative of the class of simp le asphyxiants . Boron trichloride replaces boron trifluoride because of lack of data on the latter compound. Oxygen is deleted from consideration because of its unusual properties and potential effects. 165 Similar evaluations were performed for each of the other 11 commodity categories , using appropriat e measures of hazard potential . The results of these are pres ented below , together with a brief dis cussion of the specific approach us ed . 5. Flammable Compres sed Gases The OHM data base shows 14 substanc es or types of materials to be responsible for th e 262 releases of flammable compressed gases recorded in 1976 . Four of these materials account for a total of only eight spills and can reasonably be excluded from further consideration. Three other sub stances ar e of the same chemical family and can be represented by anhydrous dime thylamine . Once NOS ma terials are deleted , the adj usted conditional probabilities are determined to be those presented below: Commodity P (adjus ted) C Liquefied Petroleum Gas ·0.827 Hydrogen 0.054 Butadiene 0.049 Ethylene 0.023 Hydrogen sulfide 0.023 Dime thy1amine 0.024 1.000 6. Flammable Liquids Flammab le liquids accounted for almost 51% of the releases reported to the OHM during 1976. Because of the wide va riety of compounds encompassed by this category , and the fact that most commodities are grouped under vague headings, such as "cement liquid NOS" (accounted • for 288 releases) , it is necessary to apply a considerable amount of judgment in the selection of materials that are repres entative . The most spills (42 . 07%) involved a single category for paints, enamels, 1acq�ers, and stains. Th e solvents us ed in these formulations include a wide range of hydrocarbons, alcohols , esters, ke tones , and glycol esters . Notably, the highly toxic solvents such as benzene, 166 te trachloroethane, and carbon tetrachloride have been largely eliminated in recent years , so the primary hazard from spills is that from fires . To "model" this group of substances , the solvent toluene is chosen as representative. It displays a moderate to high flammability hazard as well as a moderate level of toxicity . NOS ma terials accounted for 32 . 77% of releases . These are considered as materials of undefinable characteristics, so th ey are excluded from the final selection . Similarly , another 4.51% of spills are excluded since th ey involve a relatively few spills , each of a large numb er of compounds. Gasoline, kerosene , various naphthas , and other hazardous materials derived from petroleum account for 17 .18% or so of releases . To cover the category fully, it is assumed that 8.6% of spills involve gasoline , and the remainder involve xylene. Thus , both highly flammable and moderately flammable liquids ar e included. Alcohols of various types account for 3.4% of spills . Me thyl alcohol is conservatively chosen as being representative due to its toxicity and widespread use. Consol idation of these data leads to the following relationship: Commodity (adj ted) Pc us Toluene 0.673 Gasoline 0.136 Xylene 0.136 Methyl alcohol 0.055 1.000 7. Combus tible Liquids Fully 69 .2% of combustible liquid spills involve NOS materials or one or two spills each for a variety of specific substances . Th e rest involve various fuel oils , kerosene, and other basic petroleum products. Since these liquids are of relatively low vo la tility and, therefore, present negligible vapor-dispersion hazards , fuel oil No . 2 ,is selected as representative of the entire group . 167 8. Flammable Solids (Special Hazard) The 12, 063 hazardous-material incident reports contain approximately 50 involving flammable solids with unusual properties . Among those in which the hazardous ma terial is sp ecifically identified, about one half involves ph osphorus and its compounds and the other half involves sodium and its compounds . Consequently , phosphorus (11 spills) and sodium hydrosulfite (9 spills) are chosen as repres entative, and each is assigned a conditional probability of 0.5. 9. Flammable Solids (Ordinary Hazards) No more than 19 of the 12 ,063 spills involve the rather ordinary combustible ma terials des ignated as flammable solids . Becaus e of the common na ture of their hazards , and th e low in cidence of spills, this category is excluded from further consid�ration . 10 . Oxidizing Materials The 112 releas es recorded for oxidizing materials involve 36 individual commodities or type identifiers . On a gross basis, these can be segregated into the following groups : Commodity No . Spills P - c - Ammonium nitrate and compounds 38 0.3393 Others with 1 or 2 spills 23 0.2054 Oxidizing material-NOS 17 0.1518 Sodium compounds 14 0.1250 Calcium hypoch lorite mL� 11 0.0982 Nitro carbo nitrate 5 0.0446 Permanganate potash 4 0.0357 112 1.0000 After specific hazardous materials are selected as representative of subgroups , and the NOS, poorly defined , or low-frequency-of-spillage substances are deleted, the final list becomes : 168 Commodity P (adjusted) -c- - Ammonium nitrate 0.6032 Sodium chlorate 0.2222 Calcium hypochlorite 0.1746 1.0000 11 . Organ ic Peroxides Organic peroxides account for 26 of the reported spills , with 19 of them listed for unspecified ha zardous materials and the rest for two sp ec ific compounds . To represent the entire group , a single specific compound is selected; viz ., tert-buty1 hydroperoxide. It is an oxi dizer , flammab le, and may explode in fires . 12 . Poison Class A Of the 12 ,063 spills reported in 1976, only 8 invo lved Class A poisons . Phosgene accounted for four inCidents , while four other compounds each accounted for a single event . Phosgene and nitrogen tetroxide are chosen as representat ive of the group , each with a cond itional probab il ity ass ignment of 0.5. 13 . Po ison Class B Clas s B pO isons were involved in 554 releases during 1976, as follows : Conunodity No . Spills �C- NOS materials 340 0.6136 Organic phosphates 59 0.1065 Carbolic acid 22 0.0397 Dinitrophenol solution 18 0.0325 Cyanide compounds 17 0.0307 Mercury compounds 16 0.0289 Parathion 15 0.0271 Methyl parathion 10 0.0181 Aniline 10 0.0181 All others 47 0.0848 445 1.0000 169 By de finition , all these hazardous material s are usually solids or liquids . In the ca se of solids , it is difficult to envision a scenario in which there wo uld be widespread injury to the publ ic . In the cas e of liquids , however, one must be concerned with evolution of toxic vapor, as well as th e possibility of pool fires when the hazardous material is also a flammable liquid . To account for these factors, data were reviewed to determine the split between spills of liquids and those of th e solids . Th is indicated that about 85% involved liquids , while the remainder invo lved solids . Then, specific compounds were chosen to reflect the wide range of pro- perties of these hazardous ma te rials . This resulted in the lis t: Commodity (adjusted) E C Methyl bromide '* 0 . 01 § Xylene 0.20 An�'l' �n e t . 0.20 oJ. Nitrob en zene I 0.20 ell Others 0. 39 14 . Irritating Materials Spills of irritants and etiologic agents are rare . Nine were reported for all modes of trans po rtation in 1976, and even then , at least on e of th ese (the single spill listed for an etiologic agent) wa s incorrectly placed in th is category . Since it is highly unlikely for signif icant injuries to take place when irritants are spilled , this category is excluded from further consideration . * Actually a liquefied gas of high toxicity. § A representative hydrocarbon in which many toxic solids are dissolved . t A combustible liquid with toxic vapors . ell A so lid or liquid with little or no capability to disperse and/or otherwise cause harmful effects . Examples include dry solids that are non-flammab le as well as wa ter solutions of pesticides . 170 15. Corrosive Materials Of all hazardous material spills from all mod es in 1976, about 34% involved corrosive materials . For railroads alone , they accounted for about 40% of all reported releases over a multi-year period . In terms of deaths and injuries (using results from a complete mu lti-year analysis of Federal Railroad Administration (FRA) accident records) , they did no t cause any deaths , but did cause 1,555 (53%) of the 2,930 inj uries that were reported . The most common injury is a skin burn caus ed by physical contact with a co rrosive substance . Also of concern are situations in wh ich fumes from a spilled sub stance inj ure people downwind from the spill . The following results of the analysis for corrosive materials pay special attention to substances which are particularly troublesome in this regard : Commodity R (adjusted) C Phosphoric acid 0.39 Sodium hydroxide (caustic soda) 0.35 Sulfuric acid, fuming 0.15 Hydrochlor ic acid 0.10 Bromine 0.01 F. DtPACT-ASSESSMENT METHODS For each chemical group , various poss ible post-release scenarios were identified, as discussed in Section C. For each scenario , a quantitative impact model was developed. Th ese models are described in Appendix C. Input data required by each model include , among others: • Th e volume of hazardous material that is released (a random variable estimate of whose probability distribution is presented in Chapter 10) ; • Densities of ignition urceso s (discussed in Appendix D) ; and • Atmospheric stab ility conditions (also discussed in Appendix D) . 171 Fo r each category of chemicals , a condit ional scenario probability has to be assigned. In other words , given a release of ma terial in some ca tegory, if there are four mutually exclusive pos t-release scenarios, wh at is the probability of occurrence of each one? Informed estimates of these probabilities we re made and are presented in the fol lowing subsections. For most categories of materials , an examination of th e results pr esented in Section G shows that the overall impact estima tes are not sensitive to the particular choice of scenario proba bilities . The one exception is "flammable compressed gases." For this category , improved probability estimates should be made as additional information is generated over time . 1. Scenario Probabilities Scenario Scenario Probabilitv1 • Non-flammable Compressed Gases Liquid releasing with flashing 1. 0 • Flammable Compr es sed Gases Flame jet 0.30 Pool fire 0. 28 BLEVE (fireball on ly) 0.20 Vapor cloud dispersion 0.01 Vapor cloud detonation 0.01 BLEVE and rocketing 0.20 • Flammab le Liquids Pool fire 0.9 No ignition 0.1 • Combus tible Liquids Pool fire 0.5 No ignition 0.5 • Flammab le Solids Ignit ion 0.1 No ignition 0.9 • Oxidizing Haterials Detonation 0.05 No impact 0.95 172 anic Peroxides • Org Detonation 0.05 No impact 0.95 A Poisons • Class Liquid release with flashing 1.0 Class B Poisons • O. S Pool fire O.S No ignition Corros ives • Vaporization 1.0 G. SUMMARY OF IMPACT-ASSESSMENT RESULT S 1. Background This section presents the results of the overall impac t-assessment analysis. These results evolved from application of the models described in Appendix C in a manner detailed in Appendix D. 2. Non-flammab le Compressed Gases Table 12-8 summarizes results for the category of non-flammab le compressed gases . The scenario of primary in terest is the rele ase of liquid from a ruptured tank car . As it vents from the tank, some part of the liquid will flash-vaporize to form a toxic vapor cloud . The rema inder, wh ich is assumed to have cooled down to its boiling point at ambient pressure, will form a pool that boils and vaporizes continuously. The appropriate assessment models were used to address separately the initial release of vapor and th e sub sequent evolution from the pool. Results were compared and impact zon es chosen from th e set of answers associated with the greatest impac t. For selected average environmental condit ions , the weighted-average areas of potential impact for lethality, sublethal inj ury , and significant irritation are presented in th e first row of the table as a func tion of th e volume of material actually escaping from the tank . The second row similarly presents 173 TABLE 12-8 . IMPACT ASSESSMENT RESULTS FOR NON-FI.AMMABJ.E OOMPRESSIW C. ASES Probabi.- Amouut thal Zone . Inj ury Zone, (l Irritation Zone , (X I.e Cl INJ IRR Scenario lHy (gallon) (sq . km.*) L • },m .) (sq. (sq. k1ll .) I -3 -2 -2 Liquid release 1.0 1-100 8.4 10_ 1.3 10_ 2.9 x 10_ x 2 x 2 2 101-1 ,000 4.8 10 8.0 10 3 with flashing x x 7. x 10 -Average case 1,001-5 ,000 0.17 0.29 0.65 5,001-10 ,000 0.34 0.58 1.3 10 ,001-25 ,000 0.66 1.1 2.8 , 25 ,001-50 ,000 1.2 2.1 6. 7 I 50 ,001 -100 ,000 2.0 3 .7 15 .4 I ...... � -2 Liquid release 1.0 1-100 0.13 9.50 10 0. 40 x with flashing 101-1 ,000 0.88 0.67 3 .00 -Wors t case 1,001-5 ,000 3.6 2.9 18.2 5,001-10 ,000 7.9 6.8 88 . 3 I I 10,001-25 ,000 16 .9 28.2 >100 ** 25 ,001-50 .000 46 . 3 >100** >100 ** I 50,001-100,000 >100** >LOO** >100 ** - � ------� - --_. ------�� ------* = square kilometer sq. km ** Answers of this magnitude are likely to be considered error for two reasons : (1) in because 100 Values for the dispersion coefficients downw ind max imum hazard extents are greater than km. and were crudely extrapolated from datu djstances less than 100 They lDay be wrong o 0 for f r grea er dis tances ; (2) because thl.:! "worst case" wl:'athcr cond itions assumedkID . are unlikely to pers� ist fort the length of time required for dispersion to these uistances. As a consequence, the user should not accept these precictions as being completely valid . results from the mo st severe accident that could feasibly be envisi.oned. In this particular case, the material is liquefied chlorine, and it is presumed to have been releas ed during an inversion of the atmosphere, a condition which supports the propagat ion of a toxic cloud over large distances . Each of the three zones should be considered as unique regions with no overlap . For example, given the release of 75,000 gallons under typical circumstances , it should be understood that the area of potential lethality is 2.0 sq. km ; tha t the area of sublethal inj ury covers a different area of 3.7 sq. km; and that the area in which humans may be distressed, but not truly injured, is yet a different 15 .4 sq. km. 3. Flammable Compr es sed Gases Th e most difficult category to consider is that of flammable compressed gases . Depending upon the circumstances surrounding the accident, one can variously expect: • Formation of a flame jet due to ignited venting gas (literally a huge blowtorch) ; • A pool fire; • A BLEVE resulting in a fireball and a rocketing section of th e tank; and/or w A vapor cloud that disperses and result s in a vapor flash fire wh en ignited; a vapor cloud detonation; and/ or toxic vapor inhalation impact . Table 12-9 provides estimates of the average impact for flame jets, pool fires, and the fireball portion of the BLEVE as a func tion of the amount spilled. The column entitled "Probability" contains estimates of the probability that any scenario will occur, assuming that some release of hazardous materials occurs . The first and second columns for impacts provide the areas in which wooden structures may be ignited. Areas designated by 0.0 in this and following tables should be interpreted as ind icating that the impact zone is smaller than can be reasonab ly estimated (usually less than 30 sq. m. ). 175 12-9 . IMPACT ASSgSSMENl' I" OR FLAMMABLE COMPRESSED GASES TABLE RESULTS Proba- Lethal Inj ury Building Scenario hili ty ou t Zone , Zone , Damage Am n a a Zone, ap J ( ga ) (sq. kmI:) ( sq . kmI. �J (sq. km .) I L J -4 -3 -4 1. Flame jet 3 Any 1.9 10 5.9 10 1.9 10 0. x x x -4 2. Pool fire 0.28 1-100 0.0 3.2 10_ 0.0 -4 x 3 -4 101-1 ,000 2.0 10_ 3.0 10_ 2.0 10_ x 3 x 2 x 3 1,001-5, 000 1.3 10_ 1.1 10_ 1.3 10_ x 3 x 2 x 3 5,001-10,000 3.0 10_ 2.5 10_ 2.9 10_ x 3 x 2 x 3 10,001-25 ,000 6.6 10_ 5.1 10 6.6 10_ x 2 x x 2 ..... 25,001-50 ,000 1.3 10_ 0.10 1.3 10_ I ..... x 2 x 2 I '" 50 ,001-100 , 000 2.6 10 0.18 2.4 10 x x I -4 3. BLEVE 0.2 1-100 0.0 5.0 10_ 0.0 -4 x 3 -4 I (Fireball 101-1,000 1.2 10_ 5.2 10_ 1.2 10_ x 4 x 2 x 4 only) 1,001-5,000 5.0 10_ 2.2 10_ 5.0 10_ x 4 x 2 x 4 5,001-10,000 9.4 10_ 5.1 10 9.4 10_ x 3 x x 3 10 ,001-25,000 1. 7 10_ 0.10 1. 7 10_ x 3 x 3 25 ,001-50 ,000 2.8 10_ 0.20 2.8 10_ x 3 x 3 50 ,001-100,000 4.4 10 0.36 4.4 10 x x Table 12-10 presents estimates (average case) for vapor cloud dispersion and vapor cloud de tonation. For the first of these scenarios, three column s are for lethal zones in urban, suburban, and rural settings , respectively . The answers differ because of variations in ignition source densities. Similarly , three columns provide estimates for areas in which buildings may ignite due to their presence within a burning vapor cloud . The la tter scenario is .addressed in the second half of the table. In order, the impacts covered are: • Lethal inj ury to outdoor populations due to lung hemorrhage ; • Sublethal inj ury to outdoor populations due to eardrum rupture or missile impact; • Lethal inj ury to indoor populations due to building damage or collapse; • Sublethal injury to indoor populations due to building damage or collapse; • Substantial building damage ; and • Glass breakage . Table 12-11 presents estimates for impacts due to tank car rocketing . Additionally , it presents composite averages for the three settings considered. These are weighted averages us ing the probabili ties in the "Probability" co lumn . Finally , the last table of this set, Tab le 12-12, presents the worst case scenarios visualized; viz., a release of hydrogen sulfide during an inversion, and a remote accident setting in which the cloud is no t ignited while in a flammable condition. 4. Flammable Liquids The set of scenarios for flammable liquid releases is rather limited in scope . Simply stated, either the spilled liquid is ignited to form a pool fire, or it slowly evaporates to provide a toxic vapor plume problem. Results of the analysis are self-explanatory and presented in Table 12-13. 177 TAB LE 12-10. ntPAcT ASSESSMENT RESULTS FOR FLAMMABl.E COr-tPRES SED GASl�S (continued ) Urban Urban Suburban Suburban Rural Rural froba- Lethal Bldg. Fire Lethnl Bldg . Fi re Lethal Bldg. Fire Amount Zone . Zone. Zone , Zone , Zone , Zone , bUity (gal.) � (lL (lp Scenario (sq . (sq . (,!;q . (sq . � km.) km(lP9. km.) km.(lp� (sq. km" (t'q. km.� -4 -4 -4 4. 0.01 1-100 4.4 10 0.0 6.5 10 0.0 6.5 10 0.0 Vapor x _4 -4 x _4 -4 x _3 Cloud 101-1,000 6.1 10 6.1 10 ' 8.1 10 8.1 10 2.4 10 0.0 - x _3 x _3 x _3 x _3 x _3 3 dispersion 1,001-5 ,000 1.1 10 1.1 10 1.4 10 1.4 10 2.5 10 2.5 10 x _3 x _3 x _3 x _3 x _3 x _3 (w ith Dnd 5,001-10,000 1.2 10 1.2 10 2.0 10 2.0 10 4.7 10 4.7 10 x _3 x _3 x _3 x _3 x _3 x _3 wit t 10,001-25,000 1.7 10 1.7 10 2.2 10 2.2 10 5.6 10 5.6 10 hou x _3 x _3 x _3 x _ 3 x _3 x _3 ignition) 25 ,001-50 ,000 2.1 10 2.1 10 2.9 10 2.9 10 7.j 10 7.5 10 x _3 x _3 x _3 x _3 x _3 x _3 50 , 001-100 ,000 2.3 10 2.3 10 3 .5 10 3 .5 10 8.8 10 8.8 10 I-' x x x x x x ...... 00 Outdoor Outdoor Indoor Indoor Bu ilding Glass Amount Lethal Injury Lethal Injury Destruct ion Breakage ga ) (sq . ( l . km. ) (sq. km.) (sq . km. ) (sq. kill.) (sq. kill.) (&q. kill.) -3 -4 -3 -2 -4 3 3 1-100 4.4 10-4 9.6 10 1.9 10 4.5 10 .8 10 .3 10 5. Vapor 0.01 x _3 x _3 x _3 x _3 x _2 x 101-1,000 2.2 10 4.9 10 9.4 10 2.6 10 1.9 10 0.16 Cloud x _3 x _2 x _2 x _3 x _2 1,001-5,000 6.8 10 1.5 10 2.9 10 7.0 10 5.8 10 0.51 detonation x _2 x _2 x _2 x _2 x 5,001-10 ,000 1.3 10 2.8 10 5.4 10 1.2 10 0.11 (;,94 x _2 x _2 x _2 x _2 2.2 10 5.0 10 9.4 10 2.6 10 0.19 1.7 10,001-25 ,000 x x _2 x x _2 _2 3 3 25,001-50,000 3 .6 10 8.4 10 0.16 .0 10 0. 1 2.3 x _2 x x 5.8 10 0.13 0.20 0.11 0.50 4.4 50,001-100 ,000 x ---� -� -- ---.� "------TABLE 12-11. IMPACT ASSESSMEN'f RESUL'fS FOR FLAMMABLE COMPRESSED GASES (continued) Probabi- Lethal Injury Building Scenario llty Amount Zone, Zone, Damage Zone, (l (l (gal.) (sq . km.L ) (sq. kmI. �J (sq. km .) (lPD -4 -3 -3 6. BLEVE and 0.2 Any 6.10 3 x 10 3 x 10 tank car rocketing \ -4 -4 -4 Composite 1-100 1.9 x 10 1.9 x 10_ 6.9 x 10_ I. 4 3 average 101-1,000 2.9 x 10_-:e x _ 1.7 x 10_ 4 1.9 10 3 3 for urban 1,001-5,000 7.2 x 10_ 7.5 x 10_ 1.7 10_ 3 2 x 3 setting 5,001-10,000 1.3 x 10_ x 10_ x _ 3 1.7 2 2.8 10 3 I 10,001-25 ,000 2.6 x 10_ 3.4 10_ 4.8 x 10_ 3 x 2 3 25, 001-50,000 4.8 x 10_ x x 3 6.8 10_1 8.0 10_2 8.9 x x 50,001-100 ,000 10 1.2 10 1.3 x 10 ...... \0 -4 Compos ite 1-100 2.1 x 10_ 4 average 101-1,000 3.6 x 10_ 4 Same as for Approximately for 1,001-5,000 9.4 x 10_ 3 urban same as for suburban 5,001-10,000 1.8 x 10_ 3 urban setting 10, 000-25,000 3.4 10_ x 3 25, 001-50,000 6.0 x 10_ 2 50 , 001-100,000 1.0 x 10 -4 Composite 1-100 2.3 x 10_ 4 average 101-1 ,000 4.7 x 10_ Same as for Approximately 3 for rural 1,001-5 ,000 1.2 x 10_ urban same as for 3 I setting 5,001-10 ,000 2.3 x 10_ urban 3 10, 001-25 ,000 4.3 x 10_ 3 I 25,001-50,000 7.5 x 10_ 2 50 ,001-100 ,000 1. .3 x 10 ------_._- - � TABLE 12-12. IMPACT ASSESSf'fENT RESULTS FOR FLAMMABLE COMPRESSED GASES (continued ) Lethal Inj ury Ir rita tion S nari Probability A o unt Zone , Z ce o (1. Zone, one, ••. aI�J (gmal. ) (sq. a1fR (sq m:) (s«. km . km. -2 -2 -2 Worst case- 1.0 1-100 3 . 3 10 2.2 10 1.0 10_ .... x x x 2 00 H S vapor 101-1,000 0.20 0.15 6.7 10 o x c oud that 1,001-5, 000 0.78 0.60 0.27 doesi not 5,001-10 ,000 1.7 1.3 0.60 become 10,001-25, 000 3.3 2.7 1.3 ignited 25,001-50 ,000 6.5 5.5 2.6 50 ,001-100 ,000 11 . 9 10. 3 5.0 ------�------TABLE 12-13. IMPACT ASSESS�mNT RES ULTS FOR FLAMMABLE LIQUIDS Proba- I.othul Injury Hut Ion Bul ldlnu I rL' bUlty ZUIIU, ZUII!! , ZUIIC , ZUII C, Sccl... rlo AwtllUit 11J: a a llawauu III•J) ( J f�Ut (tI'l . (gut. ) (.111. kill.) (11'1, kill. � (u'l. kID. kill. ) -5 I. Ponl fJ rtf 0.9 1-100 0.0 4.0 x 10_ 0.0 fI .O 2 -4 4 -4 101--1 ,000 1. x 10_ 7.7 x 1o_ 0.0 1_2 x 10_ 4 ] 4 1,001-5,000 4.9 x 10_ ] .4 x 10_ 0.0 4.9 x 10_ ] ] 3 5,00 1-10,000 1.1 0 7.0 10_ 1.1 x 10_ x 1 _1 x 2 o.n 3 10,001-25,000 2 .5 10_ 1.5 10_ 0.0 2 .5 x 10_ II 3 x 2 3 25,001 -50 ,000 10_ ] .0 II 10_ 0.0 5.1 x 10_ �. l II 2 2 2 50,001-100,000 1.0 x 10 5.2 x 10 0.0 1.0 II 10 2 . No IUnltlun- 0.1 1-100 0.0 0.0 0.0 0.0 o -5 -5 u 101-1 ,000 0.0 5.1 x 10_ x 10_ 0.0 V p r 4 9.1 4 1,001-5,000 0.0 1.0 10_ 5.1 10_ 0.0 I!volllt ion x 4 x :1 5,001-10,000 0.0 4.0 x 10_ 1.8 x 10_ 0.0 ...... 3 3 10,01)1-2 5,000 0.0 2 . 2 10_ 3 .5 10_ 0.0 00 x 3 x 3 ...... 25,001-50,000 0.0 5.5 10_ 8.5 10_ 0.0 x 2 x 2 50 ,001-100,000 0.0 ),3 x 10 1.9 x 10 0.0 -5 1.0 1-11)0 0.0 4 1.6 10_ 0.0 0.0 C:OIllPOO Itc - x 4 -6 -4 101-1 ,000 1.1 11 10_ 7.0 x 10_ 9.3 x 10_ 1.1 x 10_ uvt:ragl! 4 ] 5 4 1,001-5 ,000 4.11 10_ x 10_ 5.1 x 10_ 4 .5 10_ x 3 1.1 ] 4 x 1 5,001-10,000 ),0 x 10_ 6.] 10_ 1.8 & 10_ 1.0 x 10_ ] x 2 4 ] 10,00 1-25,000 2 . ] x 10_ 1.4 x 10_ ] .!) 10_ 2 . ] x 10_ 3 2 x 4 ] 2 5,001 -50 ,000 4 .5 x 10_ 2 .8 x 10_ 8.5 10_ 4.5 x 10_ ] 2 x ] ] 50 ,001-100,000 9.0 x JO 4.8 x 10 1.9 x 10 9.0 x 10 -4 catlo!- 1.0 1-100 5.5 II 10_ 0.0 0.0 Wo rlit -4 3 -4 101-1 ,000 ] 2 0.0 3 .7 10_ pool fir" .7 x 10_ 4. x 10_ x 3 with xy lene 3 2 1,001-5 ,000 2 . 2 x 10_ 1.1 x 10_ 0.0 2 . 2 10_ ] 2 x 1 5,001-10,000 4.7 10_ ] .7 10_ 0.0 4.7 x 10_ x 2 x 2 2 10,001-2 5,000 1.1 x 10_ 7.] 10 0.0 1.0 x 10_ 2 x 2 25,001-50,000 2 . ] 10_ 0. 14 0.0 2 .1 x 10_ x 2 2 50 ,001-100,000 4.2 x 10 0. 26 0.0 4.0 x 10 ------5. Other Hazardous Materials Tables 12-14 through 12 -20 inclusive present results for all other hazardous-ma terial categories considered in the impact-asses sment analysis . As above, results are self-explanatory . H. REFERENCES 1. Eisenberg , N. A. , et al. , "Vulnerability Model : A Simulation System for Assessing Damage Resulting from Marine Spills ," USCG Repor t No. CG-D-137-75, NTIS No. AD-AOl5-245, June 1975 . 2. Fugelso , L. E. , et al. , "Explosion Effects Computation Aids ," General American Research Division, General American Transpor tation Corporation , Niles , Illinois, June 19 72, GARD Proj ect No . 1540, AD903279 . 3. "The Effects of Nuclear Weapons," Glasstone, S., ed. , U.S. DOD , U.S. GPO , Washington , D. C. , 1962 . 4. White, C. S., liThe Nature of the Prob lems Invo lved in Estimating th e Immediate Casualties from Nuclear Explosions," Lovelace Foundation for Medical Educat ion and Re search , Albuquerque , New Mexico , March 1971 , CEX 71 .1 5. Lawson , D. 1. and S imms, D. L. , "The Ignition of Wood by Radiation ," Brit. J. Appl. Phys., 1952 , pp . 288-292. 1, 6. Mackison , F. W., et al. , "NIOSH/OSHA Pocket Guide to Chemical Hazards ," Department of Health, Education and Welfare, NIOSH, Public No. 78-210 , Septemb er 1978. 182 TABLE 12-14. IMPACT ASSESSMEN1' RESULTS 1,'OR COMUUS'fIBLE LIQUIDS Proba- Lethal Inj ury Buildlng Scenario Amount Zone. bllity Zone . Q Zone. Q Dumage Q (gal. ) (sq . km.L ) kmI. �J (sq. km .) pD (sq . -4 1. Pool fire 1-100 0.0 1.5 10_ 0.0 0.5 -4 x 3 -4 (also worst 101-1.000 1.2 10_ 2.0 10_ 1.2 10_ x 4 x 3 x 4 I case) 1,001-5.000 6.2 10_ 7.4 10_ 6.2 10_ x 3 x 2 x 3 5,001-10 .000 1. 7 10_ 1.8 10_ 1. 7 10_ x 3 x 2 x 3 10, 001-25,000 4.0 10_ 3.5 10_ 4.0 10_ I x 3 x 2 x 3 25.001-50, 000 8.2 10_ 6.7 10 8.2 10_ x 2 x x 2 50.001-100 ,000 1.6 x 10 0.12 1.6 x 10 ..... 2. No ignition 0.5 Any 0.0 0.0 0.0 c;, w -5 Composite 1.0 1-100 0.0 7.5 16_ 0.0 -5 x 5 -5 average 101-1,000 6.0 10_ 6.0 10_ 6.0 10_ x 4 x 3 x 4 1.001-5 ,000 3.1 10_ 3.7 10_ 3.1 10_ x 4 x 3 x 4 5,001-10,000 8.5 10_ 9.0 10_ 8.5 10_ x 3 x 3 x 3 10 ,001-25 .000 2.0 10_ 1.8 10_ 2.0 10_ x 3 x 2 x 3 25 ,001-50. 000 4.1 10_ 3.4 10_ 4.1 10_ x 3 x 2 x 2 50 ,001-100.000 8.0 10 x 6.0 x 10 8.0 x 10 Worst case 1.0 See Scenario 11 1 above -�--� TABLE 12-15. Il-tPACl' AS SI�SSHENT FOR FLAl1HABLE SOLIDS (SPECIAL HAZARD) Prob�- Letha l InJ ury Build ing Scenario bility Amount Zon Damage Zune, e, a Zone , a apD I (lb . ) L I�J (sq. km.) (sq. km . (sq. km.) - 4 -3 -4 Burning railroad 0.1 Any 1. 2 10 2.3 10 1.2 10 1. x x x car 2. No ignition 0.9 Any 0.0 0.0 0.0 -5 - -5 Composite 1.0 Any 1.2 10 4 x 2.3 10 1.2 10 ..... x x 00 average J:o. -3 -3 -4 Wors t case 1.0 See Scenario 1.2 10 2.3 10 1.2 10 x x x III above 'fABLE 12-16. IMPACT ASSESSMENT RESULTS FOR OXIDIZING MATERIAl.S I'rol.u- Outdoor hllJuor Oul ...... r fuduor lIu lldlng 1l�5 Gl u:ltI " UI'uakagc , !iel:nil r b y I.ulhal, " Inj.u·y , " , Injury, " " 10 U l l Aauwlt - ,. ItU ... thul , uL INI In.eLJ &H' , 1'1 "" I (gal . 1 .J- 10 ) (Sl, . km. ) (';11· "'.... ) (UII . km.) (5'1. km.) . (I.UI. IuD.) (s" . kill.) 3 3 -Ie - - -Ie -] -2 J. llulunalioll 0.1 1-100 8. 7 x ICl_ 1.9 x 10_ ].7 10_ _ � ] ] It 2 9.0 x 10 ] 7. x 10-2 (l,(' II 10 ( re'lul hl:ut 101-1,000 Ie 1. 7 10 r�s Ie.1x ICl_ 2 9 . 7 II 10_2 1.9 x 10_2 .O x 10_2 x 0. 32 or tlhoek � O lO to I, - , x 10_ ].1 10_ 5.7 x x lO_ 0. 12 1.0 OOI OO I.] 2 x 2 Lie 2 oceua-) �,OOI-lO,OOO 2 .5 10 5 2 0.2 1.9 x _2 5. x 10_ 0.11 .0 x 10_2 1 2 Ie.O 10,001-2 5,000 JO_ 9.7 x 10 0.19 II 10_ 0.17 ].2 Ie.]II 2 2 - 2 5,001 50 ,000 7.� II 10 0.17 0.31 7.0 II lO 0.62 5.Ie 50 ,001-100 ,000 0.11 0.48 0.le9 0.11 0.98 8.6 ..... 00 Nu Any VI 2 . 0.9 0.0 0.0 0.0 0.0 0.0 0.0 'lulonat!on - CoIllj,ulIll.. -5 -Ie 4 -5 -4 -1 1.0 1-100 11 .7 II 10_ 1.9 x 10_ ].7 II 1 0_ 9.0 x 10_ "/.) x 10_3 b.b x 10_ 4 Ie ] 4 3 2 Avera!;&: 101-1 ,000 4.3 x 10_3 x 10_3 1.9 II 10_3 4.0 x 10_, ].7 x 10_ . 2 II 10_ 9.7 ) 2 1 1,001-5 ,000 1.1 II 10_3 ].1 II 10_3 5.7 II 10_3 1.4 x 10_3 1.2 x 10_ l.0 II 10_ 2 1 5,001 -10,000 2 .5 II 10_ 5.5 x 10_ 1.1 x 10_ 2 .0 x 10_ 2 .1 x 10_ x 10_ 3 1 2 3 2 1.9 1 10,001-2 5,000 4. II 10_ 9.7 x 10_ 1.9 II JO_ 4.0 It 10_ x 10_ 3. 2 II 10_ '1 1 2 2 1 1.7 2 1 25,001-50 ,000 7.2 x 10_ 1.7 x 10_ 3.1 x 10_ 7.0 10_ 6.2 x 10_ 5.4 x 10_ 2 2 2 II 2 2 1 50,001- 100 ,000 1.1 x 10 4.8 x 10 4.9 II 10 1.1 II 10 9.8 x 10 8.6 II 10 Wo r"t Casto Se&: Sc.:uariu '1 above . �- " 1'h 1ll S 'llc! fltolt u unul yultl wall orlglnully butled un alllOunLtI I l PUUIII'II . Tu facllltute a'I,'rulIIII�aL f lUie , thl! IIIIIUWlttl werll convur led to glllluUII using .UI I! eOllvertiJon uc tor . TABLE 12-17. IMPACT ASSESSMENT RESULTS FOR ORGANIC PEROXIDES OUldooe Outduoe Indoor Indoor �ul ldJ Ilg Ilu.. - Glllu,; Iltu.. '1'lOba- AlllUllnl II In luey, l ulu, y, ,uet JUII, 1 ..:, 1 ... 1 , I L S.:unarlu blU" . 1..." h" I, ul "IIU CI" U k.lgc. (gnl.) (UII . ) ulNJ . tll"�) k .... (u'l . 1un.) ( ,.., k ....) (:;11 . k",. ) (U(I ' kID.) (:;'1 . kill. -4 -1 -4 -] 1. 0.1 1-100 6.tI lO_'i 1.5 10_ .. 2 .!I x JO 1.0 x 10_ 5.11 10_ 5. 1 l\ - flt:tunuttoll x x = 3 x 2 111 · (n",ul ru,; heul 101-1 ,000 1.1 x 10_ 1.7 x 10_ 1.4 x 10_� 1•• 0 x 10_ 2 ,. 9 x 10_ 11. 25 or uhock to 2 2 2 2 2 1 ,001 ··5 ,001) J.O x 10_ 2 .4 x 10_ 4.4 x 10_ 1.1 x 10_ 8 .9 x 10 O. "/II ul'eur) 2 2 2 2 5,001-10 ,000 ) . 9 10_ 4.] x 10_ tI.2 10 I.K 10_ O.lb 1.4 x 2 2 x x 2 10,01) 1-2 5,0011 3.4 10_ 7.6 x 10 0.14 1•• 0 x 10_ 0.2!1 . ;) x l 2 2 I' 2 5,00 1-50 ,000 5.6 10_ 0.12 0.24 6.0 10 •. 0.4t1 4.2 x 2 x 2 SO ,OUI-I00,OOIl 8.8 It 10 0.2 7 0.18 9.1l 10 0. /6 6. (, I-' x (Xl 0\ 2. No O.OJ Any 0.0 0.0 0.0 11 .11 11 .0 11.11 Ilt:lollat Jon -5 -4 -5 -5 -4 6.8 10_ l. 2 -] t:ulllj",.. lle 1.0 1-100 It 5 x 10_ .9 x 10_ 7.0 x 10_ x 10_ S.l 10_ 4 4 3 4 :'1.11 1 x 2 Ave,"ug..: 101-1,11011 :J .1 x 10_ 7.7 It 10_ 1.4 10_1 '•• 0 x 10_ 2 .9 10_ 2 .5 10_ 1 1 x 1 x 1 x 2 1,001·'5 ,0110 1.0 111_ 2 IO_ x ) .4 x ' 4.4 x HI _ 1-1 x 10_ 8.9 x 10_ 1.8 x 10_ J 3 1 2 1 5 ,OIH -10,000 1.9 10_ 1 4."J II 10_ tI.2 x 10_ 1.8 x 1.6 lU_ x 1 2 JI)_ x 2 1.4 x 10 2 l 10,001- 5,1100 "J .4 II 10_ 1.b II 10_ L4 x 10_ 4.0 x 10_1 2 .9 x 1t1_ 2 .5 1 2 2 2 x 2 2S,IIOI -:'IO ,O(l() :'.6 x IO_' 1. 10_ 2 .4 x 10_ 6.0 x 10_ 4.8 x 1Il_ W=: J x 2 2 3 2 4.2 x HI_ 50 ,0111-100,000 8.8 10 I x 2.7 l\ 10 1.8 x III 9.0 x 10 7.6 x 111 6.6 x 10 Sc.:narlo bov\: . I 1I.... st lSee II .. ':UtiU � 1'AB LE 12-18 . ASSESSMENT IMPACT HESUL'fS FOR ('1 .ASS A POISON Proba- Lethal inj ury Irr1tatlon I Amount Zone , a Zone, a1 Zone , a1 R Scenario bility � rJ f I (gaL ) (sq. km. (sq. km . (sq. km. -3 ':'2 -2 I 1.0 1�100 5.7 10_ 5.4 10 7.6 10 I Liquid release x 2 x x 101-1,000 7.1 10 0.78 1.2 I with flashing- x I 9.6 Compos ite 1,001-5,000 0.47 5.8 30.8 average 5,001-10,000 1.3 18.1 10 ,001-25,000 3.7 53.2 94 .4 25,001-50,000 9.3 > 100* > 100* 50 ,001-100 ,000 22.4 > 100* > 100* -2 I 1-100 4.23 10 0.49 0.83 Liquid release 1.0 x 12.1 25.9 ,I with f1ashing- 101-1,000 0.71 I 1,001-5,000 6.6 >100* >100* ..... Wo rs t case ! 00 (phos gene) 5,001-10,000 24 .8 >100* >100* ...., 10 ,001-25 ,000 92.4 >100* >100* 25 ,001-50,000 >100* >100* >100* 50 ,001-100 ,000 >100* >100* >100* * (1) Answers of this magnitude are likely to be considerably in error fo r two reasons : becaus e 100 downw ind maximum hazard ex tents ar� grea t�r than km. Values for the dispersion coefficients 100 a and a wer e crudely ext rapolated from data for distances less than km . They may be wrong (2) f r gre ter distances; becaus e th e "wors t case" wea ther cond itions assumed are unlikely to persis� t Xfor the length of time required for disper sion to these distances . As a consequenc e, th e user should not accept these predictions as being completely valid. � ....,. N , !"I I == I � I0000 t""'I I , ---_ ... - >C >C >C >C >C 0000000 0000000 ,...... -�oo ...... = C-� too: �-:���CO N�-.... :i=:i:i=== =QOQQC ..:: , i! "'" =':00000 ==:::0 == ===��QC ...... :.. :! .:. ==00=== ��q�======::: �� ======:======- � 2 '4' !""'I �NNN , !""'I N I I 000I I I000 I =0 I -- _ ...... lC lC lC �-:-... =""'"..... "'O�N .... ����� f""t N"'=Q=-:�� ��,..: �c-\�e ,...... � ..... ���r-"'NN ""��:"""I ('II,I N �:-"'I N N ..,; . ',1'\ c-'", '" , , I = I 00I :: I I I 00==I I =00=I I I I I 0 I 00I I 00I 0 I I - � --- - - a 00- - ... ------"'" - == )( ,. ,. ,. ,. ,. >C lC >C ... :I >C >C >C >C >C >C >C >C lC lC lC >C >C >C j ... J"\:O_�_""..,, 0 = ,...,, :'\ .... :ooo. _ N �:'\"'QQN ...... �1 ...... :'\0:: . . :II). .t'\�. .."':: ...... ::0 5 ..... -:- 0 = .:! �"-" O-OCI<" �-- - ..... -:- ..:r-'>:N'.t"I _ :-"t" NN -� � -�J -oo % = oooS= = :2 0 g 0-08 o. = -. co = = = - .. -0 _= 3 = Q . = 0g8gg8° · 0•• .... 0-c ;,. S5.. � g �= 0=. - -0 tI'\ = o • N ... :0 -0 '.1'\ � __"'_'!"o.a""'- -;"f\_N\I'\, _ _I .... � _ "" I I I I t I --- .. - -I - I , I I I I I I I I ====�O - Q. = C -;;o- = a== = -;=::. . === .. . . ", .. =. =. . =. e. .. Q. -==:== - ..., 0 ..., 0 _101'\= ,,",0 - ...... , -N'" ,.. ::I ...... 0 - "" = . .. .::I ... = 0 �. - :.' ." ..I " ... :I 'l ! � ...... 'l ' � - :) ...:I � :I -:I... :I ].. ... � ' ... iI ' 3 :.I . ;:-:- '::.I ... :II ' ...... :: ..� :: .. - ... i ... - :.I S :) � :.0...... :; ::" :I.. J g a :) : ... 11 ...... � ... � - '" :I 1- = !""' = > .." :II :. ..., � :J ' :I 2 1/ :i :i ;; ..:> fo if' .i "i - N a :i 188 TABLE 12-20 . IMPACr ASSESSMENT RESULTS FOR CORROSIVES Scenario Proba- Amount Lethal Zone� il Inj ury Zone�Il Irritation Zone� L INJ bi1ity (gal. ) (sq. (sq. km .) (sq . km.) IlIRR km.) -4 -3 Liquid release 1.0 1-100 0.0 3.9 x 10_ 1.5 x 10_ -5 3 2 with vapor 101-1 �000 6.1 x 10_ 4.8 x 10_ 2.2 x 10 4 2 evolution - l�OOl-s � OOO 3 .7 x 10_ 3.1 x 10 0.16 3 -2 Composite average 6,001-10 ,000 1.0 x 10_ 8.83 x 10 0.50 3 10 ,001-25, 000 2.7 x 10_ 0.24 1.5 3 2S�001-S0 ,000 6.5 x 10_ 0.61 4.0 2 50,001-100,000 1.5 x 10 1.4 10.2 -4 -2 2.1 x 10_ 2.0 x 10 0.11 Liquid release 1.0 1-100 3 101-1,000 2.3 10_ 0.25 1.6 with vapor x 2 1,001-5 ,000 1.3 10_ 1.7 12 .0 � evolution - x 2 co 5,001-10, 000 3.6 x 10_ 5.0 37 .8 \0 Wo rs t case 2 - 10 �001-2s �000 9.3 x 10 13.9 >100* � (bromine) \0 2s �001-50 ,000 0.22 36.1 >100* o SO �001-100 �000 0.49 87 .0 >100* '*An swers of this magnitude are likely to be considerably in error for two reasons: 1) hccau�e downwind maximum hazard extents are greater than 100 km. Values for the dispersion( coefficients O and were crudely extrapolated from data for distances less than 100 km. They may be wrong x C1 for grea er distances; ( 2) because the "worst case" weather conditions assumed are unlikely to persist lfor the length of time required for dispersion to these dis tances . As a consequenc e, the user should not accept these predictions as being completely valid. APPENDIX A &� OTATED BIBLIOGRAPHY As part of this proj ect, Arthur D. Little, Inc. , assemb led a Proj ect Resource Library. Th is library contains do cuments and data tapes that are required for the proj ect , as well as do cument s that describe research and information related to this proj ect. In reviewing the documentation for the Proj ec t Resource Library, an annotated bibliography was completed and is provided on the fo llow ing pages . The bibliography has been arranged into five general categories . They are : 1. Risk and Safety , 2. Hazards and Hazardous Materials : Transportat io n, Consequences , Safety Analysis , 3. Rail, Railroad , Ra ilcar: Mechanical Tests and Analysis, 4. Association of American Railroads/Railway Progress Institute (AAR/RPI) Track Car Safety Research and Test Proj ect. 5. Miscellaneous . A-l 1. Risk and Safetv. Arthur D. Li t tle , In c. , IIEstimation of the Frequency and Cos t Associated 'N ith the Cleanup of Hazardous Materials Spills ," for Environmental Protection Agency , Contract Number 68-01-3857, Draft Final Report , Sep temb er 1978. Th is report es timates th e cost to the Federal Governmen t for effor ts to contain , clean up and dispose of contaminated ma terials ; restore the environmen t; and monitor spills of hazardous materials . It considers releas es of solids , liquids, and gases to all media. Stoehr , L. A. , et a1 ., IISpill Risk Analysis Program: Methodology Developmen t and Demonstra tion--Final Report Volume I,ll Operations Research , Inc. , for Department of Transportation (DOT) , Report Number CG-D-2l-7 7, Final Report, April 1977 . The report describes methods for ass es sing th e effectiveness of merchant marine safety regulations . Analytic modeling involves phys ical parameters ; vessel size , speed, maneuvera bility ; and human res pons es . Logical modeling of casualties addresses the effects of changes in regulations . White , tv . D. and Stoe hr , L. A. , "Spill Risk Analys i.3 Program : Hethodology Development and Dell'.o nstration--Final Report , Volume II," Operations Research , Inc. , for Department of Transportation , Report Number CG-D-22-77 , Final Report , April 1977. (See previous entry.) Simmons , J . A. , "Risk Assessment of Storage and Transport of Liquefied Natural Gas and LP Gas ,1I Science Applications . Inc . for Environmental Protection Agency (EPA) . Contract Number EPA-68-0l-2695, November 1974. Described is a method for assessing the societal risk of transporting liquefied natural gas (LNG) or liquefied petroleum gas (LPG) by truck and ship . Data on past experience and proj ected handling of the liquefied gases are used with flammab le plume analyses to estimate the risk of fatalities from liquefield gas shipments . Comparison with fires and explosions from all causes shows a relatively low frequency of LPG-LNG accidents . A-2 Philipson , L. L. , "Risk Analysis in Hazardous. Materials Transportation : A Mechanism for In terfacing the Risk Analysis Model with the Hazardous Materials Incident Reporting System," University of Southern California for Office of Hazardous Materials , Report Numb er TES-20-74-6, Final Report September 1974 . This report describes the risk analysis system of the Office of Hazardous Materials ; dis cusses the system's advantages and shortcomings , and recommends improvements. The present system makes risk analysis , predicts expected shipping losses, an d provides comparative risk evaluations , based primarily on the data of the Hazardous Materials Incident Reporting System. Philipson , L. L. , "Inves tigation of the Feasibility of the Delphi Tel:hnique for Estimat ing Risk Analysis Parameters," Un ivers ity of Southern California, Research Center , for Office of Hazardous Materials , Report Number TES-20-74-4 , Final Report, April 1974. The report examines the potential for augmenting the data base for a hazardous transportation model through an organized · survey of experts . Th e Delphi experiment wh ich was conducted is described and a Bayes procedure for comb ining statis tical data with the Delphi results is also defined. Jones , G. P. , Barrow, R. W. , Struckenb ruck , L. C. , Holt, E. L. , and Keller, R. P. , "Risk AnalYSis in Hazardous Material Transportation , Volume I," University of Southern Califo rnia, for the Office of Hazardous Mat erials , Report Numb er TES-20-73-4-l, Final Re port, March 1973. A risk analysis model is developed and demons trated through twenty examples to show its flexibility in accepting data , and the types of results . A demonstration was performed to show the practicality of evaluat ing special permit petitions . Jones , G. P., et al., "Risk Analysis in Hazardous Materials Transportation , Volume II , Bibliography ," University of Southern California , for Office of Hazardous Materials , Report Numb er TES-20-73-5-2 , March 1973. Section 1 of the bibliography contains ab stracts . Section 2 contains a concise bibliographic lis ting . A-3 National Transportation Safety Board , Special Study , "Risk Concepts in Dangerous Goods Trans portation Re gulation ," Report Nwnber NTSB-STS- 7l-l , January 19 71 . Th e study examines the salient approaches underlying th e development of exis ting regulations , the difficul ties created by regulations , and the needs which mus t be met by new approaches . Th e NTSB concludes th at a risk-bas ed framework for future regulation is necessary, desirable, and feas ib le. Simmons . J .A•• et a1 . , "Risk Assessment of Large Spills of Toxic Materials ," from Proceedings of the 1974 National Conference of Control of Hazardous �mterials Spills , San Francisco, California, Au gust 1974. S immons, J. A. , et a1. , "Risk of Catastrophic Spills of Toxic Chemicals ," California University , Los Angeles , for Energy Research and Development Administration , Contract Number E(04-3)-34 , May 19 74. Berger , R. W. , "Us e of Risk Ana lysis for Decision-Making," in Compu ter Decisions , March 1972. National Res earch Council, Committee on Hazardous Materials , "Proceedings: Conference on Hazard Evaluation and Risk Analysis ," for Un ited States Coast Guard (USCG) , 1971. Daenzer , B. J. , "Fact-finding Techniques in Risk Analysis," American Management As sociation, New York , 1970 . Garrick, B. J. , Baldonado , O. C. , and Gekler, W.C. , "E stimating the Risk Involved in Transport of Hazardous Materials ," Minutes of th e Explosives Safety Saminar , Memphis , TIT ., August 25-27, 1970 , Armed Services Explosive Safety Board , Was hington , D. C. , 1970 . Transportation Systems Safety Research Group, University of Illinois , "Development of Risk Methodology for Transportation Systems Safety," Report of Tasks 1, 2, and 3 to Department of Transportation , Washington , D. C. A-4 2. Hazards and Hazardous ��te�ials : Transportation, Consequences, Safety Analys is Buckley, J. L. , et a1. , "Hazardous Haterials SpUls : A Do cumentation and Analysis of Historical Data ," Factory Mutual Research Corp. , Norwood, Mas s ., for EPA-Office of R&D, Report No. EPA-600/2-78-066, April 1978. The obj ective of this study was to provide guidance for the choice of research priorities for spill prevent ion through documentation and analysis of historical incidents involving hazardous-ma terial spills . Data were analyzed for the period January 1, 1971 through June 30 , 1973. To allow comparison of spills of different materials, a hazard potential scheme was developed . Incorporating toxicity and quantity spilled, incidents were ranked on a hazard potential scale ranging from one to ten. The scheme developed is specific to the needs of this study rather than being a general mechanism for comparing spills . Primary and secondary causes of hazardous material spills in various operational areas (in Transit, Loading-Unloading Areas , in Plant Storage , in Plant Processing) were identified . Th e data were treated to find the frequency and dis tribution of hazardous-material spills by cause, operational area, and hazard potential. "Hazardous Materials Transportation--Part 1: General Studies (A Bibliography with Abstracts) ," Period Covered : 1964-1977 , National Technical Information Service (NTIS), Report No . PS-77/040S, June 1977. The transportation of explos ives , rocket propellants , chemical warfare agents , industrial chemi cals , liquefied natural gas , chlorine, and other hazardous materials is covered. All means of transportation are described. Accidents, economics, and statistics are also included in these reports . Radioactive wastes and materials are excluded . (This up dated bibliography contains 243 abstracts , S3 of which are new entries to the previous edition.) "Hazardous Materials Transportation--Part 2: Radioactive Materials and t-la stes Bibliography with Abstracts) ," Period Covered : (A 1964-1977 , NTIS Report No . PS-77/0406, June 1977. The bibliography presents studies on the hazards , risks , and uncertainty of transporting radioactive wastes and materials . The design of shipping containers and special labels for identification pur poses for transporting fuels and wastes are als o cited. Studies are included on legislation dealing with the safety and health of the population and the environmental problems associated with transporting radioactive materials . (This updated bibliography contains 130 abstracts , 24 of which are new entries to the previous edition.) A-S Hende rson , N. C. , et a1 ., "Survey Study of Techniques to Prevent or Reduce Discharges of Hazardous Chemicals ," Battelle Columbus Labs ., Ohio , Final Report , NTIS Report No . AD-A020 173/1st, August 1975. A program was conducted for the Office of Research and Development , U.S. Coast Guard , to inves tigate both off-the shelf and conceptual techniques for preventing or reducing the discharge of hazardous chemicals from an endangered marine vesse1, or to stop or reduce the discharge from an actual leak . First, approximately 50 methods and/or types of equipment were identified. Next , the compatibility of each of the concepts and equipment with the Chemical Response Information System (CHRIS) list of hazardous chemicals was determined on a relative basis . The concepts were then evaluated on the basis of their relative chemical compatibility in comb ination with overall usefulness and the various types of on-site operations to which they applied . Allan , D. S. , and Harris , G. H., "Chemical Response Information System for Mu1timoda1 Accidents (CHRISMA) --A Reevaluation of CHRIS for All Modes of Transportation ," Arthur D. Little, Inc. , Cambridge , Mass., Final Report , NTIS Report No . AD-A0 16 296/6 ST, Ap ri l 1975. This report examines the need for improved technical and other information for meeting emergencies connected with the transportation of hazardous materials , particularly actual or potential chemical discharges, regardless of mode . The Chemical Hazards Response Information System (CHRIS), under development by the United States Coast Guard to furnish in-depth guidance during emergencies involving waterborne transport, was seen as a likely prototype for other modes as well. It is concluded that the expanded system would indeed be beneficial in reducing losses to life , property , and the environment . Jaquette , D. L. , "Possibilities and Probabilities in Assessment of the Hazards of the Importation of Liquefied Natural Gas," Rand Corp., Santa Monica, California , NTIS Report No. AD-A019 353/2ST, April 1975. There are at least four main research areas that mus t be addressed in developing estimates of the risk to population and property from the importat ion of large quantities of LNG . Th e report examines the available research approaches directed toward one of these, the assessment of the pO$sib1e release scenarios and , in particular, their associated probab ilities. The character and need for more research are discussed. A-6 Atallah , S. , et a1. , "Supplement--Task III: Summary of LNG Safety Research," Arthur D. Little , Inc., Cambridge , Mas s ., for DOT/Office of the Secretary of Transportation (OST) -Office of Pipeline Safety , Report No. PB273378, December 1974. Results from major published research programs related t o assessment and alleviation of potential hazards LN are described . Topics covered include : vaporizG ation and dispersion from spills , boiling heat trans fer LN rates for LNG on wa terG, superheat "explosions ," tank stratification and rollover, thermal radiation from pool fires , detonation conditions , pool sp read and u� thGermal radiation from ignited releases on water , LNG ------. deflagration of natural gas-air vapor clouds , and L� fire control and suppression research . In addition Gto descriptive material, an extensive bibliography is included and future research needs are sugges ted. Fridinger, C. E., et. a1. , "Development of Performanc e-orien ted Specifications for Drums and Pails for Packaging of Hazardous Materials for Tra nsportation ," Naval Surface Weapons Center , Silver Springs , MD, for DOT , Office of Hazardous Material , Final Report No . PB 240 647 , December 1974. Hazard classifications , performance requirements and tes ts , and a container rating system were developed . The rationale behind the development is presented in the report . Test plans for qualification and periodic testing and detailed test procedures were prepared . Tes ts inc luded were leak, distortion , press ure-proof, repetitive f:hock (vibration) , west strength-stacking, �rop , puncture, and temperature cycle . A representative sample of drums and pails now regulated by DOT was subj ected to the test program. Details of the test results are included in the report . Lind , C. D. , "Explos ion Hazards Associated with Spills of Large Quantities of Hazardous Materials"--Phase I: Naval t-leapons Center , China Lake , California , for USCG, Washington , D.C. , Final Report , NTIS Report No. AD/A-OOl 242 /75L , October 1974. The report documents the results of Phase I of a program wh os e obj ect is to quantify the explos ion hazards associa ted with spi lls of large qu ant ities of hazardous ma terial such as liquefied natural gas liquef�ed petroleum gas (LN ), (LPG) , or ethylene. The princG ipal results are :(l) a pheno menological description of a spill , (2) an exami nation of the detonation properties of methane, (3) a qualitative theory of non-ideal exploSions , and (4) a plan for Phase II of the study . A-7 Va ssalo, F. A. , et al. , "Review of Proposed Specifications Relating to the Shipmen t of Ethylene in Tank Cars at Cryogenic Temperatures ," Calspan Corp. , Buffalo , N.Y. , for DOT/Federal Railroad Adminis tration (FRA) , Office of R&D , Final Report No . FRA-OR4D 25-41, September 1974. This report reviews proposed specifications and shipper regulations for 113 series tank cars for transporting l�quid ethylene at cryogenic temperatures . The study was limited in scope and was to be directed primarily at the holding time requirements necessary for safe shipment of the commodity . Apparent deficiencies are noted in the proposed in-transit pressure rise specification ; a candidate modification is described . Arthur D. Little , Inc. , "A Modal Economic and Safety Analysis of the Transpor tation of Hazardous Subs tances in Bulk ," for U.S. Depart ment of Commerce , Maritime Administration , Report No. C-76446 , May 1974. The obj ective of the study was to analyze quantitatively the economics and safety of transporting selected bulk hazardous substances , other than oil , by inland waterway and overland (rail, truck, and possibly pipeline) modes , so that the costs and risks associated with the different modes could be compared. There were three maj or components to this process: (1) choosing the substances , origin-designation combinations , and shipment characteristics to be studied; (2) determining all costs involved in transporting each substance between the designated points by barge and relevant overland modes ; and (3) determining the frequency and quantity of spills likely with each mode and the resultant risk to people, property , and the environment. Lyman, W. , et al, "Survey Study to Select a Limited Number of Hazardous Materials to Define Amelioration Requirements--Vols . I and II," Arthur D. Little , Inc. , Cambridge, Mass. , for USCG Office of R&D , Washington , D. C. , Final Report, NTIS Report No. AD/A-004 3ll/75T , March 1974. The work entailed the categorization of hazardous chemicals according to physical and chemical characteris tics that were perceived to be amenable and important to the development of amelioration techniques. A total of 400 hazardous chemicals deemed to encompass most of the more critical chemicals in terms of quantity shipped and the severity of the hazards presented were associated wi,th each of approximately 30 amelioration categories . A representative chemical was then selected for each category with the intent that it would provide the basis for searching for , evaluating, and develop ing amelioration methods from each category . The represen tative chemicals were chosen by assessing the chemical and physical behavior of the chemicals , their risk indices , and other practical considerations . A-a Lippian , J. X. , "The Transportation of Hazardous Materials : Transport of Benzene by Tank Car ," Intern Training Center , U.S. A�y Materiel Command, Texarkana, Texas, Master's Thesis , NTIS Report No . AD77ll0S, May 1973. Specific recommendations on the identification and labeling of the hazards associated with benzene are discussed and a risk rating model is sugges ted for general use in the transportation of hazardous materials . Through use of a gross hazard analysis and a fault tree analysis , the basic parameters involved in the transport of benzene are determined . Lasseigne, A. H. , "Hazard Classification of Explosives , Flammable and Oxidizing Materials for Transportation--Evaluation of Test Methods," G.E. Apollo and Ground Systems , Bay St. Louis , Miss., for DOT/Office of Hazardous Materials (OHM) , Final Report , NTIS Report No . PB225 422, May 1973 . The work described herein correlates proposed explos ives testing with proposed tes ting for the classification of other related types of hazardous materials--inorganic· oxidizers , organic peroxides , and flammable solids . The work also provides information relative to additional hazard classi fication testing, further refinements in hazard classification test methodology, and expanded hazard classification test criteria. "U. S.C.G. Oil Pollution Investigation and Control School: On-Scene Coordinators Manual, " C.G. Reserve Training Center , Yorkt own , Va ., NTIS Report No . AD-758-Sll, Novemb er 1972 . The report is a handbook for a Federal On-scene Coordinator for use in combating oil and hazardous-material spills . It includes the National, Regional, and Local Contingency Plans , guidelines for the coordinator , and a case study of an oil spill involving the USNS Towle in New York harbor . "U.S.C.G Oil Pollution Inves tigation and Control School: Investigator' s Manual," C. G. Reserve Training Center, Yorktown, Va ., NTIS Report No . AD-758,510, Novemb er 1972. The report is a handbook for water pollution investigators . It includes applicable laws , the Miranda case, criminal investigative procedures , report writing guidelines , sample reports , photographic techniques , evidence gathering, and an outline of tanker/terminal oil transfer operations . A-9 Ra th , G. J. , et a1. , "A Study of Hazardous Materials In formation Needs and Identification Systems for Transportation Purposes ," Northwes tern University Design and Development Center, Evanston, Ill. , for DOT/OHM, Final Report No . TSA-20-72-4 , May 1972. Information needs and me thods to transmit that information are an alyzed to determine the basic requirements of a hazard identification system for packages containing , and vehicles carrying, hazardous materials . Persons who come in contact with hazardous-material shipments are identified and a typo logy developed . Information needs (type, amount, and timing) are listed by category , and sixteen existing labeling systems are evaluated according to these and human factors criteria. Environmental Protection Agency , Wa shington , D.C. , "Control of Hazardous Material Spills ," Presented at the Proceedings of the National Conference on Control of Hazardous Material Spills , Hous ton , Texas , NTIS Report No. PB-228 736/5, March 1972. Contents in clude: The protection of the environment from hazardous-material spills ; prevention of hazardous ma terial spills in heavy process indus tries ; contingency planning for response to hazardous-material spills ; the containment of hazardous material spills ; th e detection and identification of hazardous-material spills ; treatment systems for waters contaminated by hazardous materials ; the effects of hazardous ma terial spills on the environment; ecology restoration of waterways following hazardous-material spills . Ostrem, F. E. , and Libovicz , B., "A Survey of Environmenta l Condit ions Incident to the Transportation of Materials ," General American Transportation Corporation, Niles , Ill. , for DOT/OHM, Final Rep ort No. 1512-1, October 19 71. A survey was conducted to compile , analyze and summarize environmental data defining the transportation environment. The current availability of information describing the conditions of vibration , shock, impact, heat , cold, compression, puncture, abrasion, humidity and temperature is assessed and significant data presented . Summaries of the data are given to show the extremes of the environmental conditions for each element of the transportation cycle (in-transit, storage and handling) where possible . A-lO Bullerdick, A. , et a1. , Study to Reduce the Hazards of Tank Car toJ' . "A Transportation ," Cornell Aeronautical Lab . Inc. , Buf falo , N.Y. , for DOT/FRA, Final Report No. FRA-RT-71-74, November 1970 . Principal obj ectives were to (1) define thermal inputs and associated vapor generation ra tes for hazardous ma terials transported in tank cars when subjected to fire exposure ; (2) develop performance speci fications and conceptual design and application requirements for safety devices preventing catastrophic car failures; and (3) formulate a research program for the design and tes t verification of recommended safety devices . Prime effort was directed toward the prevention of catastrophic rupture of large-capacity, pressure-type cars . A number of shortcomings with exis ting safety-relie f specifications were indicated. A staged safety relief system was recommended for cars with liquefied compressed gas ladings . Dawson , G. toJ' . , et a1 ., "Control or SpU1age of Hazardous Polluting Subs tances ," Battelle Memorial Institute, Richland , Washington , NTIS Report No . PB-19 7 596, November 1970. An evaluation of the water quality aspects germane to the spillage of hazardous polluting substances is developed. Emphasis is placed on definition and clas sification of chemi cal materials ; the nature of the source of spillage and pas t experience; analys is of the relative threat to water quality offered by such substances ; a review of pres ently available detection , control , and remova l technology , and their relationship to water quality standards ; and the relevant administrative, enforcement, and cost-recovery as pects . Over 250 chemicals and compounds , generally those in large scale production and utilization , are priority-ranked in order of relative threat to wa ter quality . "Control of Hazardous Polluting Substances ," U.S.C.G, Washington , D.C. , Final Report , NTIS Report No . PB-199 193 , October 1970 . This study deals with only the water pollution aspect . Focus was placed on accidental spills and effluent discharges in excess of those authorized. The study supports a report on the need for legis lation to impose liability and financial responsib ility requirements for the cost of removal of hazardous subs tances discharged from vessels and onshore and offshore facilit ies . In addition, the study includes an extensive bibliography . A-ll Booz-Allen and Hami lton , In c., Washington , D.C., "An App raisal of th e Problem of the Handling , Transportation, and Disposal of Toxic and Other Hazardous Ma terials ," for DOT, Final Report, NTIS Report No. PB-236 599/ 7ST, January 19 70 . The report presents detailed narrative , tables , and graphs as follows : Hazardous-ma terial clas sification ; types and quantities of hazardous ma terials ; accidents involving hazardous ma terials ; transportation environment; disposal of hazardous materials ; and references and contacts . Hazardous materials discussed are flammab le materials , compressed gases , corrosive materials , explosives, oxidizers , pistons including chemical warfare agents and pesticides , infectious agents, radioactive materials , and molten materials . Nationa l Academy of Sciences , Washington, D.C. , "A Study of Transportation of Hazardous Materials ," Study Group at Warrentown, Va ., NTIS Report No. AO-692 182 , May 1969. This report cons titutes the findings of a study undertaken May 7-9 , 1969, for the specific purpos es of appraising existing knowledge, procedures , and practices of all trans portation modes ; exploring imp roved or revised concepts for approach to regulations , based on scientific knowledge and engineering me thods ; and suited to the practices and materials of an increas ingly technological culture; identi fying existing and new resources and facilities needed to support more technology-oriented approaches to public safety regulation ; and recommending immediate and longer term actions for improving the present regulatory system for hazardous materials transportation . A-12 �ational Highway Traffic Safety Administration/Materials Transportation Bureau (NHTSA/HTB), "Emergency Action Guide for Selected Hazardous �Iaterials ," DOT , 1978. Raj , P. K. , "Calculation of Thermal Radiation Hazards from t.."iG Fires A Review of the State-of-the-Art," Paper presented at the AGA Transmission Conference, St. Louis , Mo., May 1977. DOT , "First (through Seventh) Annual Report of the Secretary of Transportation on Hazardous Materials Control," Washington, D.C. , 1970- 19 76 . Ar thur D. Little, Inc., Cambridge , IIResponse by Re gulated Indus try in Terms of the Degree of Prevention and Associated Cost Relative to the Hazardous Substance Portion of Section 311 of the FWCPA Amendments of 19 72 ," for EPA , Final Report, December 1976 . u. S.C. G. , "A Manual for Safe Handling of Flammable and Combus tible Liquids and Other Hazardous Products ," DOT , Report No. CG-174 , September 1976. Robertson, F. A. , "Fire Standards and Safety," Symposium conducted at the National Bureau of Standards, Gaithersburg, MD. , ASTM Special Technical Publication 614 , April 1976. Porter , C. H. , "State Program Implementation Guide: Hazardous Was te Transportation Control," EPA , Washington , D.C. , Report �o . EPA/530/SW-5l2 , March 19 76. EPA, Washington , D.C. , "Development Document for Hazardous Substance Regulations ," Draft Report , January 1976. Wiggins , J. H. , "Discussion that Accompanies the Briefing on Technology Assessment of the Fire Hazard in the Occupant Compartments of Various Transportation Modes ," Redondo Beach, California , April 19 75. Material Kalelkar, A. 5., et a1. , "Decision AnalysiS in Hazardous on Control Transportation ,"Proceedin�s of the National Conference rnia, of Hazardous Materials Spi lls, San Francisco, Califo August 1974. Hazards • ative Spill ge 11 , G R and Kalelkar , A S. , "The Co st and Rel An • • ,. Materials , " Related with the Modal Transport of Hazardous e on Control of Hazardous Proceedings of the National Conferenc fornia , August 19 74. Materials Spills , San Francisco, Cali A-13 American Insurance As sociation, Engineering and Safety Service, N.Y. , "Special Loss Control Bulletin and Chemical Hazards Committee," Bulletin No. 14 , October 1973. Back, A. A. , et al. , "Reclassification of Materials Listed on Transpor tation Health Hazards Supplement ," Aerospace Medical Lab , Wright Patterson AFB , Oh io , Final Report , September 1973. Arthur D. Li ttle , In c. , Cambridge, Ma ., "Radiation from LNG Fires ," Reference No . 73854 , Augus t 1973 . Maej awa , M. , "Experiments on Fire Hazards of Liquefied Flammable Gases ," Japan Society of Safety Engineering, May 19 73. Streblow, R. A. , et a1. , "On the Measurement of Energy Release Rates in Vapor Cloud Exp losions," University of IllinOiS , Aeronautical Engineering Department , 1972. Univers ity of Engineers , Inc. , "LNG Vapor Dispersion and Fire Tests," A joint effort sponsored by the Philadelphia Gas Works , Walter R. Kidde Co. , American Gas Association , Oklahoma , December 1971. Fine , W. T. , "Mathematical Evaluation for Controlling Hazards ," Journal of Safety Research , Vol. 3, No. 4, pp . 157-166 , December 1971. Atallah, S., and Allan , D. S. , "Safe Separation Distances from Liquid Fuel Fires ," Fire Technology, Vol. 7, No . 1, pp . 47-56, 1971. Arthur D. Little , Inc. , Cambridge , Ma . , "A Report on LNG Safety Research- Vol. II ," prepared for American Gas Association, Proj ect 742-1, 1971. Association of American Railroads , "Report of the Chief Inspector of the Bureau for the Safe Transportation of Explosives and Other Dangerous Articles ," Report Nos . 55 through 61, 1961 through 19 68. Fizer , J. C. , "Transporting Hazardous Materials by Rail ," Classic System Huntington , W. Va. (article) . American Gas Association , "Con sequences of LNG Spills on Land , " L.'l G Safety Program, Phase II. U.S.C.G. , "Hazardous Chemical Data," Report No. CG-446-2, Vol. I-IV. A-14 3. Rail, Ra ilroad, Railcar: Me chanical Tests and Analyses James , R. K. , Chairman , "Special Safety Inquiry : Imp roved Safety Standards for Insulated Pressure Tank Cars , " Hearing convened by FRA, Transcrip t of Proceedings published by Acme Reporting Co ., Washington , D.C. , April 1978 . The subj ect of the hearings is the need to improve present safety standards for the design and cons truction of new and exis ting DOT Specification IDS-insulat ed pressure tank cars . James , R. K. , Chairman , "Special Safety Inquiry : Retrofitting Timetab le for 112/114 Uninsulated Pressure Tank Cars , " Hear ing convened by FRA , Trans cript of Proceedings published by ACME Repo rting Co ., Washington , D.C. , Ap ril 1978. The purpose of the hearing is to ob tain information on whether it is possible to speed up the schedule for ins tallation of special safety devices on uninsulated pressure tank cars . Peters , D. , and Yin, S. K., '�on-Destructive Impact between Railroad Cars: Experimental and Analytical Study ," School of Engineering and Applied Science - Washington Univ. , St. Louis , Mo ., for DOT/FRA - Office of R&D, Rept. No . FRA-ORD-76/247 , January 1977. A computer simulation of the dynamics of rail car impacts is compared with experimental data obtained from full-scale switchyard impacts . The compared cases involve impacts between a standing light hopper car and a moving, fully loaded tank car at speeds ranging from 2 mph to 8 mph . The monitored dynamic responses include ver tical car motions , draft gear travel , longitudinal coupler forces , car body ac celerations , and vertical bolster loads . Johnson , M. R. , "Development of Performance Specifications for LPG Tank Cars", IIT Research Inst. , Chicago , Ill. , for DOT/FRA , Cont . No . P.O. 74282, Final Report, January 1977 . The Material Transportation Bureau has proposed requiremen ts that l12A and l14A tank cars be equipped with a thermal protection system, a tank head puncture res istance system, a safety relief va1ve , and a coupler res traint system. The spec1. fic requirements for each of these systems are defined by performance standards. Over the last several A-IS years results have been ob tained from a number of research programs which have been conducted to study various aspects of the tank car safety problem. The relationships of these results to the performance standards which have now been proposed for the tank car safety systems ar e described. "Final Standards , Classification, and Designation of Lines of Class I Railroads in the United States", Vols . I and II, Dept. of Transportation, January 1977. This report follows a thorough public review of the Preliminary Standards Classification and Designation of Lines of Class I Railroads in the United States published by the Department on Augus t 3, 1976, pursuant to Section 503 of the Railroad Revitalization and Regulatory Reform Act· of 1976 (P .L. 94-210) (the Act) . The review process was conducted by the Rail Services Planning Office of the Inters tate Commerce Commission which culminated in their publication of an Evaluation Report of the Secretary of Transportation's Preliminary Classification and Designation of Rail Lines . This Evaluation Report, along wi th the public tes timony elicited at the hearings,was considered by the Department in preparation of this Final Report. Volume I of the Final Report es tablishes five standards for the classification of the Class I rail system: (1) density, (2) service to maj or markets, ( 3) appropriate levels of capacity , (4) national defense, and (5) line potentially subject to ab andonment under statutory and ICC procedures . Final Volume II contains designations of all Class I Railroad lines in the United States based upon the standards developed in Final Volume I. Each Class I Railroad line segment in the national rail ne twork was subj ected to individual analysis , using the mos t current information availab le . Designation and identification of individual line segments in the U.S. railroad network structure are presented using a computerized ne twork information system. Statistical summaries of route mileage by line designation are presented. Cross-reference information is presented . Also, an enlarged fold-out national network map displaying the line designations by category is provided. A-16 Johnson, M. R. , IIEvaluation of Proto type Head Shield for Hazardous Material Tank Car ,1I IIT Research Institute, Chicago , Ill., for DOT/FRA-Office of R&D, Final Rep t. No . FRA/ORO 75/96, December 1976 . The structural integrity of a pro to type tank car head shield for hazardous material railroad tank cars was evaluated under conditions of freigh t car coupling at moderate to high speeds . Tes t data were obtained when the car was impacted into standing cars over a 3- to 9 mph speed range. The tes ts produced no visible damage to the shield or the struc ture " connecting it to the tank car, but they demons tra ted the presence of severe vibrations resulting from the car impact. The likelihood of fatigue damage was indicated in the connecting structu ral members where the weight of the shield was supported . Hahn , E. E. , "Increased Rail Tr ansit Vehicle Crashworthiness in Head-On Collisions ," IIT Research Institu te, Chicago , Ill. , for DOT/TSC, Contract No . DOT-TSC-1052, August 1976 . ABSTRACT . A computer code for mo deling the collision of two consists of urban railcars was developed. This code was used to es tablish the critical parame ters which govern whe ther the cars will crush, displace vertically and override, or crush with subsequent override . The draft gear shear pin failure load , spring cons tant and travel as well as the an ticlimb er horizontal force characteris tics were found to be important parameters . A complex and a simp lified model of two impacting consists were modeled and run on the computer. It was concluded that accura te results could be obtained from a simplified model. Acceleration pulse shapes were obtained,suitab le for use in determining the nature and severity of passenger inj ury in a head-on collision . Tong , P. , "Mechanics of Train Collision" , DOT/TSC, Cambridge , Mass ., for DOT/FRA - Office of R&D , Final Rept. No . FRA-OR&D-76-246, April 19 76. A simple and a more detailed mathematical mo del for the simulation of train collisions is presented . The study presents considerable insight as to the causes and consequences of train mo tions in impact. Comparison of model predictions with two full scale train- to-train impact tes ts shows good correlation . Me thods for controlling train mo tion and kinetic energy dissipation for the minimization of train co llision-induced damage are sugges ted . A-17 Peters , D. A. , et a1 . , "Tank Car Head Puncture Mechanisms School of Engineering and App lied Science - Washington Univ. , St. Louis , Mo ., for DOT/ FRA, Rep t. No . FRA-ORD-76/269 , Final Report , June 1976 . This report is concerned with the descrip tion and analysis of head puncture mechanisms . Three classifica t ion yard ac cidents and one main line accident were studied in detail, train-to- train co llision tes ts were analyzed and the results of impact experiments were evaluated . The main conclusion of the report is that head puncture in classification yards is invariably due to overspeed impact. Lee , E. H ., and :!allett, R. L. , "Structural Ana lysis and Design for Energy Absorp tion in Impact," Division of Ap plied Mechanics - Stanford Univ. , Stanford , Calif., for DOT Office of Un iversity Research (OST) , Final Rept. No . DOT-TST-76-44 , December 1975. A general assessment of the nature of the dynamic problem of an alyzing the collision of a vehicle is given . Elas t ic-plas tic theory is used . Theo rems are given which provide approximations to the maximum plas tic deformation and the duration of plastic flow without determining the who le solution. Application of these to simp le models is presented . The ability of porous metal to absorb energy of deformation is also analyzed by solving the microscopic problem of collapse of the cavities . Tests of the behavior of porous metal in imp act are presented and related to quasis tatic measurements of its deformation properties . Kennedy , R. G. , and Lloyd , F. H ., "A Me thodology for Evaluating the Economic Im pacts of Applying Railroad Safety Standards Vo ls . I and II , CONSAD Research Corp ., Pittsburgh , Pa. , for DOT/FRA , Final Rept. No . RP-4l, October 1974. This report presents an evaluation of safety standards proposed by the Federal Railroad Adminis tration and allows for detailed analysis of individual equipment, track, and human fac tors stand ards . Dis cussions are given of other aspects of the methodology such as the proper analysis time span , the effects of inflation and interest rates , quantification problems and the role of sens itivity analysis . Special at tention is given A-18 to accidents and accident prediction and also to data availab ili ty and data acquis ition. An examp le is given of the use of the methodology using the safety standards addressed to plain bearings on freight cars . Volume 2 of this report is the manual whose step-by-step procedures are intended for the implementation of economic impact analysis . In developing this manual , high priority was placed on presenting wo rkable procedures that can be used immed iately for economic impact evaluation . Special attention is given to accidents and accident prediction , discounting, quantification problems and the role of sensitivity analysis . A completely worked example is presented in the appendix. Association of American Railroads (AAR) Advisory Committee , "Car and Locomo tive Cyclopedia ," (a third ed ition) Simons-Boardman Publishing Corporation, N.Y. , 1974 . Defini tions and illus trations of railroad cars and locomo tives and their components built for domes tic and export service , including shop practices and electrical fundamen tals . Ad ams , D. E. , et a1 ., "Rail Hazardous Material Tank Car Design Study," Ca1span , Buffalo , N. Y. , for DOT/FRA, Contrac t No . DOT-FR-20069 , Prelim . Rep ort , Calspan Rept. No . ZL-5226-D-4 , Ap ril 1975 . This report provides th e basis for defining prac tical and economical safety imp rovemen ts and identifies the safety research gaps wh ich mus t be close d before a pro to type tank car can be designed to op timal safety/economic considerations . Six areas were given particular cons ideration because of their greater po tential for success for ll2A/ ll4A series tank cars. These were : (1) operational changes , (2) head shields, (3) modified couplers , (4) thermal insulation , (5) tank material changes , and (6) safety relief sys tem modifications . Head shields and mod ified ial ." couplers were found likely to be "cos t-benefic proved Other tank car research is reviewed and an im on a tank thermal mo del for calculating the effects tantial car exposed to fire is presented . Subs be feasible improvements in car safety appear to materials or wi thout resort to the use of exo tic no t be fabrication techniques which could manu facturing accommodated by existing tank car facilities . A-19 Wilkinson, M. T. , et al . , "A Structural Study of Rail Tank Cars ," Louisiana Tech University , Rus ton , La ., for DOT/F��, Contract No. DOT-FR-30056, June 1975. A review and evaluation of the present specifications under which tank cars are des igned is made from a structural viewpoint . Deficiencies in these specifications are reported and specific mo difications ar e recommended. The results of a finite elemen t mo del and an experimental model of a quarter scale DOT l12A340W car are reported . These results demons trate that stresses calculated by simple beam mo dels of tank cars are no n-conservative . Finite element analyses are also included on full-scale DOT III and DOT 112 cars . These studies show that these cars fail to satisfy the present design requirements in the AAR specifications . Hohenemser , K. H. , et al ., "Computer Simulation of Tank Car Head Puncture Mechanisms Classification Yard Ac cidents , " School of Engineering and Ap plied Science - Washington Univ. , St. Louis , Mo. , for DOT/FRA Office of R&D , Prelim. Rept. No . FRA-OR&D-75-23 , February 1975. Development of means for identifying possible puncture me chanisms and quantifying the coupler fo rces involved is the subject of this report . A mathematical model , capable of simulating train ac tion in the vertical plane , has been developed and used for simulation of three classification yard accidents . A detailed description of the mo del and the results of simulation are presented. The conclusions of this report mus t be considered tentative until the resul ts of verification studies become available. Adams , D. E. , "Cost/Benefit Analysis of Thermal Shield Coatings Applied to 112A/ 114A Series Tank Cars , " Calspan Co rp. , Buffalo , N. Y. , for DOT/FRA - Office of R&D, Final Report, Rep t. No . FRA-OR&D 75-39 , Decemb er 1974. This report updates the analysis done by AAR/RPI on aCCident losses . His torical data for insulated l05A tank cars were compared with uninsula ted ll2A/l14A tank cars . Results indicate that the "efficiency" e., expected effectiveness) of the (1. A-20 thermal shield appears to be nearly 100 percent- at least in the critical hours . Computer calculations of the temperatures and pressures produced in tank cars have in dicated that significant reductions in tank rup ture are expected for even thin insulations if the insulation remains attached to the tank during the fire . Townsend , W. , et a! . , "Comparison of Thermally Coated and Uninsulated Rail Tank Cars Filled with LPG Subjected to a Fire Environment," Ballistic Research Labs . - U.S. Army , Aberdeen Proving Ground, MD , for DOT/FRA - Office of R&D , Final Rept. No . FRA-OR&D 75-32, December 1974. Two fire tes ts were conducted on l28-kiloliter , high-pressure rail tank cars filled wi th liquified petroleum gas . Both tank cars were exposed to an intense hydrocarbon fire after being outfitted wi th appropriate ins trumentation . The ins trumentation was monitored and its output recorded throughout the fire tes ts . To tes t the feasibility of insulating railroad tank cars to protec t them from fire exposure, one of the cars was coated with a 0.318 centimeter (em) thermal shield . comparison of data conclusively shows that a Athe rmal shield significantly alters the thermal response of a rail tank car in a fire environment. Anderson , C. , et al ., "The Effects of a Fire Environment on a Rail Tank Car Filled with LPG," Ballistic Research Laboratories - U.S. Army , Aberdeen Proving Ground , MD . , for DOT/FRA Office of R&D , Final Rep t. No . FRA-OR&D 75-31, September 1974. A 127 kiloliter (33, 600 gallon) railroad tank car was instrumented and filled with liquefied petroleum gas . A large JP-4 fuel pool fire then engulfed the ' tank car , and measurements of temperature, pressure , etc. , were recorded as a function of time . After 24 .5 minutes , the car failed catas trophically via stress-rup ture. Mass flow rates and a discharge coefficient have been obtained for the relief valve . An analy tical expression has been derived and then used to ob tain the heat flux to the wetted surface of the tank car. A-21 Anderson , C. , and Norris, E. G ., "Fragmentation and Metallurgical Analysis of Tank Car RAX 201" , Ballistic Research Labs - U.S. Army , Ab erdeen Proving Ground , MD. , DOT/FRA - Office of R&D, Final Rept . No . FRA-OR&D 75-30 , Ap ril 1974. On 28 July 1973 , the Ballis tic Resear ch Laboratories performed a full-scale fire test on a 33 , 000-gallon, DOT l12A340W non-insulated , pressure , rail tank car for the Federal Ra ilroad Adminis tration and As sociation of American Railroads . The car was filled with liquefied petroleum gas (LPG) . After 24.5 minutes of exposure to the fire, the tank car ruptured. This report concerns the mapping of the fragments and me tallurgical analysis of the ruptured car , along with an inves tigation of the cause and initial location of failure . Adams , D. E. , et a! ., "Cost/Benefit Analys is of Head Shields for ll2A/1l4A Series Tank Cars , " Calspan Corp. , Buffalo , N.Y. , fo r DOT/FRA - Office of R&D , Final Rep t. No . FRA-OR&D 75-34 , March 1974. This analysis was based on a redistribution of accident dollar losses using data from AAR/RPI. His torical data are too limited to provide the co rrect dis tribution of losses between head and shell punctures . Supporting evidence is presented indicating that dollar losses are strongly related t.o puncture distribution for a more extensive set of data including all classes of tank cars . It was concluded that head shields on new and existing ll2A/ l14A pressure-type tank cars would be cost beneficial . An derson, C. , et a!. , "Railroad Tank Car Fire Test: Tes t No . 7," Ballistic Research Laboratories - U. S. Army , Aberdeen Proving Ground , MD., for DOT/FRA - Office of R&D, Final Rept. No . FRA-OR&D 75-37, December 1973. A fire test was conducted on a one-fifth scale model pressurized railroad tank car on 7 February 1973. The tank car model had a thermal insulation of 4 inches (10 .16 cm) of polyurethane encased in a 0.12S-inch (0.3lB-cm) steel jacket. The mo del was loaded with propane and then engulfed in a JP-4 jet fuel fire. A-22 Anderson , C. , et al ., "Railroad Tank Car Fire Test: Tes t No . 6, " Ballistic Research Labs - U.S. Army , Ab erdeen Proving Ground , MD. , for DOT/FRA - Office of R& D, Final Rep t. No . FRA-OR&D 75-36, Augus t 1973 . The Department of Transporta tion is conducting an extensive research program designed to develop methods to minimize personal injury and damage to property caused by fire from ruptured railroad tank cars filled with hazardous materials . The Ballis tic Research Laboratories were requested by the Department of Transportation to conduct a series of field tests with scaled mo del and standard-size railroad tank cars . The test described in this report is one of the scaled model series which had no thermal protective coating , and where the relief valve was turned ninety degrees from the vertical . Levine , D. , and Dancer, D. �1 ., "Fire Protection of Railroad Tank Cars Carrying Hazardous Materials - Analytical Calculations and Laboratory Screening of Thermal Insulation Candidates ," Naval Ordnance Lab. , White Oak , MD. , for DOT/FRA, NTIS Rept. No . AO- 747 974, July 1972. This report describes a laboratory screening program to select two thermal insulation candidates for us e in future fire tes ts of fifth-scale and full-scale LPG tank cars . Also included are analy tical calculations to predic t pressures and liquid levels in LPG tank cars being heated by fires . (Author) Everett, J. E., and Phillips , E. A., '�azardous Materials T��k Cars - Tank Head Protective 'Shield ' or 'Bumper ' Design, " AAR , Chicago , Ill. , for DOT/FRA , NTIS Rep t. No . PB-202 624-1 , January 19 7 2. The objective of the study was to design a railroad tank car head protective device which will reduce the frequency of head punctures in accidents . Accident data were reviewed in detail for the pas t six years to correlate head damage frequency and severity with various types of cars , to determine distribution patterns of damage over head surfaces , and to assess the costs to the railroad shipping indus try of head punctures . F ull- scale head impact tes ts , previously run , were also reviewed. From these two reviews , design criteria were established and used to design a large number of schemes which were then subjected to a comprehensive cos t/benefit analysis . (Author) A-23 AAR Research and Test Department, "Coupler Steel Study , " Chicago , Ill. , AAR pt.Re No . R- I07 , December 1970. This report presents the results of a preliminary study of the properties of "c" and "E" steels in "F" couplers selected at random from stocks about to be utilized by railroads . Class "E" couplers were also inves tigated . The data in this report do not cons ti tute a random sample of the properties of steel in couplers , but they do indicate the characteris tics of the several couplers that were studied . "The Dynamics and Economics of Railway Track Sys tems ," an International Fo rum published by Railway Sys tems and Management Assoc., Chicago , Ill. , February 1970. Presents ten papers : "Railroad Track Structures - Current Progress and Future Plans !!; "Track and Truck!! ; "Track for Today 's and Tomorrow 's Vehicles"; "Moura Railway - Queens / and Governmen t Railways!! ; Transport Work on the Swedish Railways !! ; "German Federal Railways"; "British Railways" ; "Unconventional Railway Track Support Sys tems" ; liThe Influence of Track Dynamics on the Des ign of Advanced Track Structures" ; "Service Tes ting Concrete Ties in the Search for Op timum Track" . A-24 Addi tional Re ferences Materials Transportation Bureau , "Specifica tion of Pressure Tank Car Tanks" , DOT, Washington , D. C. , Federal Register (49 Parts 173 , 179) Docket No . HH- 144 , November 1976. AAR Operations and Maintenance Department - Hechanical Division , "Specifications for Tank Cars , Standard" , l.rashington, D.C., July 19 76 . FRA Office of Research , Development and Demons tration, "Impact Properties of Steels Taken from Four Failed Tank Cars," Washington . D.C. , Final Rept. No . FRA-ORO 75�1 , June 1976. Railway Progress Ins titute Committee on Tank Cars , "Petition for Advanced Notice of Proposed Rulemaking," Before the Materials Trans portation Bureau , DOT , Washington , D.C. , March 1976. FRA , "A Comprehens ive Railroad Safety Report (including an Analysis of the State Participation Program) ," Special Report to the President and Congress , Washing ton , D.C. , Rep t. No . FRA/RSS-760l , March 1976. "Comparison of Various Thermal Systems for Pro tection of Rail Tank Cars Tes ted at the FRA/BRL To rching Facility, December 1975. Hicho , G. E. , and Brady, C. H ., "Hazardous Materials Tank Cars - Evaluation of Tank Car Shell Cons truction }la terial ," for DOT/FRA - Office of R&D, Final Rep t. No . FRA/ORD-75-46, September 1975 . Manufacturing Chemis ts Assoc. , "Ethylene Oxide Tank Cars ," for DOT - Secre tary . Hazardous Materials Re gulations Board , Summary Report, Augus t 1971 . Clevenson, S. A. , and Ullman , K. B't "A Technique for Evaluating Track Condition Using Railcar Vibra tions Paper presented at the AIAA/ASME 12th Structures , Structural Dynamics and Materials Conference , Anaheim, Ca . , Ap ril 1971. Meyers , E. T. , "Track Analysis Car Guides on Maintenance," Mo dern Railroads , Vo l. 25 , No . 10 , pp . 62-63 , October 1970. United States Steel Railroad Facts , "Axles wi th Improved Fatigue Strength ," Ap ril 1969 . AAR, "Field Impact Tes t of Loaded Freight Cars ," Specification No . 73544.4. ... A-25 4. AAR/RPI--Tank Car Safety Research and Test Proj ect Reports Skogsberg, A. M. , and Ph illips , E. A. , IIPhase 11 Report on Inspection of Insulation Jacket Type Th ermal Shields on Tank Cars in Ac celerated Life Tes ts ,1I RPI-AAR Tank Car Safety Research and Tes t Proj ect, Ph ase 11, Report No . RA- 11-9-39 , January 19 78. Four l12A tank cars were retrofitted wi th one inch mineral fiber ins ulation and a steel jacket and subjected to ac celerated life tes ting. Inspections at the en d of the tes ts revealed nothing to indicate that this type of ins ulation could not maintain its integrity for the life of a tank car . Porter , R. t.J . , IIEvaluation of RPI-AAR and BRL Torch Fire Tests of Tank Car Insulation ,1I RBI-AAR Tank Car Safety Research and Test Project, Phase 11 , Report No . RA-11-8-36, September 1976. This report compares the torch fire tes t apparatus developed by RPI-AAR with that of the Ballis tic Research Laboratory through tes ts on laboratory scale and full-size tank car wa ll structures . The report concludes that while the two apparatus do not yield entirely cons is tent results , the economy and repeatability of tests with the RPI-AAR equip ment indicate that they should be adopted for thermal shield qualifying tests. Ph illips J E. A. J Chairman , IICommunication Session of Petition of RPI Committee on Tank Cars J II pres ented at Palmer House , Chicago J April 19 76. These are the minutes of a symposium which reviewed the work of RPI-AAR Tank Car Safety Proj ect and the DOT activities in that field. Also presented is a petition to the DOT concerning proposed rulemaking . Railway Progress Institute (RPI) , Committee on Tank Cars , "Petition before the Materials Transportation Bureau , U.S. Department of Transportation," March 15, 1976. While the petition contains references to several proposed rulings and to res earch done by various agencies , the main thrus t of th e petition is to permi t conversion of existing ll2A and l14A tank cars to an improved insulated design , and to approve the ins tallation of head shields . A-26 RPI/AAR Railroad Tank Car Safety Res earch and Test Proj ect , "Technical Progress Report No . 31, Interim Report ," February 1976. Progress in the various tasks of the RPI-AAR effort is briefly discussed. Of particular interest are remarks made in res pons e to FRA and NTSB recommendations . Also included is a tabulation of accidents and 1% waybill data for hazardous materials . E. Phillips, A. , and Skogsberg , A. M. , "Phase 11 Report on Specifications for Thermal Shield Systems on DOT ll2A (114A) Tank Cars ," RPI-AAR Tank Car Safety Research Proj ec t, Report No . RA- 11-7-34 , January 1976. Over 100 laboratory tes ts and several full-s cale tes ts were conducted to measure the effectiveness of various tank car ins ulating materials . The report concludes that the labora tory apparatus should be used in developing acceptance criteria for thermal shielding . Phillips , E. A. , "Phase 05 Report on Head Shield Fatigue Tes ts ," RPI-AAR Tank Car Safety Re search and Tes t Proj ect , Phase OS , Re port No. RA-05-3-35 , November 1975. TheRP I-AAR Tank Car Safety Proj ect conducted a series of tes ts to one-half-inch thick head shields for railroad tank cars . From the data obtained, in-s ervice life predictions were made for each of four attachment schemes . This report des cribes th e study and recommends proposed specifications for head shield attachment designs . RPI/AAR Railroad Tank Car Safety Research and Tes t Proj ect, "Track Train Dynamics Report--Volume II--Harmonic Roll Series." Report No. R- 1 73, February 1975. A documentation of the American Steel Foundries 'work in developing characteristics of the 70-ton truck components , physical restraints , mechanical properties , etc. RPI/AAR Railroad Tank Car Safety Research and Test Proj ect , "Track Train Dynamics Report--Volume III--Harmonic Ro ll Series , " Report No . R-174 , A document dealing with work done by the Track-Train-Dynami cs Program to develop comprehensive vehicle models to predict dynamic behavior and perform parametric studies . Also included in this document is work done by A. S tucki Company to evaluate the effect of eccentric loading on the roll tendencies of various vehicles . A-27 RPI/AAR Railroad Tank Car Safety Re search and Tes t Proj ect , "Track Train Dynamics Report : Engineman 's Sensitivity Studies ," Transportation Sys tems Center , Cambridge , Mass ., Report No . R-188. The report documents experimental studies of the respons e of enginemen to va rious physical stimuli . RPI/AAR Railroad Tank Car Safety Research and Tes t Project, "Track Train Dynamics Report : Track-Train Dynamics Guidelines ," Report No . 185. This book contains guidelines for optimum handling , train makeup , track considerations , etc. The results are based on a parametric study using validated analytical models . RPI/AAR Railroad Tank Car Safety Research and Tes t Proj ect , "Track Train Dynamics Report : SUlIUJlary of Phase I Activities ," Report No. 180. This is a general overview of the work done in both the experimental and analytical areas designed to achieve Phas e I obj ectives . De tails of individual activities are contained in specific books or manuals dealing with that subject. RPI /AAR Railroad Tank Car Safety Research and Tes t Proj ect, "Track Train Dynamics Report : Accident Investigation," Re port No . 175. Recommended procedures for determining the cause of dynamically related derailments and other accidents. Pellini, �., . S., Eib er, R. J. , and Olson , 1. 1. , "Phase 03 Report on Fracture Properties of Tank Car Steels--Characterization and Analysis ," RPI-AAR Tank Car Safety Research and Tes t Project, Phase 03, Report No. RA-0 3-4-32 , August 19 75. Statis tical examination of fracture properties of tank car steels indicates that brittle fracture is not a significant prob lem. A clear relationship has been demonstrated between ASTM Ferrite grain size and dynamic tear test rational criteria. RPI /AAR Railroad Tank Car Safety Research and Test Project, "Track Train DynamiCS Re port--Volume I--Harmonic Roll Series ," Report No. R- 172, November 1974. A compreh ens ive review of the problem, relationship of track and car design to the problem, recommended guidelines , based on best of the present knowledge, etc.). A-28 Mate, D. P. , and Ph illips , E. A. , "Phase 10 Report on Development of Shelf Couplers ," RPI-AAR Railroad Tank Car Sa fety Research and Tes t Proj ect, Report No. RA-10-5-30 , Septemb er 1974. Contained in th is report is preliminary des ign and test data compiled by a coupler foundry, outlining the strength and fabrication complexities of shelf couplers . Photographs and tes t des criptions are included. The report concludes that shelf couplers would prevent mos t overriding and telescoping of train cars under conditions approximat ed by the tests if those couplers are properly mated. Reedy , G. E. , "Phas e 05 Report on June 9, 1974 Accident Involving Head Shield$ ," RPI-AAR Railroad Tank Car Safety Res earch and Test Proj ect , Report No. RA-OS-2-29 , Augus t 19 74 . An ac cident involving one car equipped with a head shield is examined. In that accident, the head shield performed well; puncture was avoided . Furthermore , the shield attach ment appears adequate. One additional conclusion is that F couplers are essentially ineffective in preventing head damage. Krauskopf, W. B. , "Final Report on Phase 09 Ext ens ion Study of Tank Car Bottom Fittings ," RPI-AAR Railroad Tank Car Safety Research and Tes t Proj ect , Report No. RA- 09-2-27, May 1974 . Accident inves tigation has shown that the bottom fittings are the mos t vulnerable components of tank cars . This report contains a cost benefit analysis and a number of recommendations for improving th e resis tance of bottom fittings to damage and leakage . RPI/AAR Railroad Tank Car Safety Research and Test Proj ect, "Phase 10 Report on February 9, 1974 Accident Involving Type E Top and Bottom Shelf Couplers ," Report No . RA- 10-4-28, April 1974 . This is a report of an accident involving a tank car which was equipped with Type E shelf couplers . During the derail men t, the couplers remained intact and prevented puncture of the tank car head. The report includes photographs of the couplers . A-29 Phillips , E. A. , "Phase 10 Report on July 1, 1973 Accident Involving Type E Top and Bot tom Shel f Couplers ," RPI-AAR Railroad Tank Car Safety Res earch and Tes t Project , Report No. RA- 10-3-2S, Decemb er 19 73. The role of shelf couplers in an accident involving th e derailment an d puncturing of loaded tank cars is examined. The report concludes th at the shelf couplers performed better than standard couplers would be expected to do , although one accident is not statistically signi ficant. RP I/AAR Railroad Tank Car Safety Research and Tes t Proj ect , "Track Train Dynamics Report--Track-Train Dynamics "Bibliography", Report No . R.19l, March 1973 . A three-volume publication outlining in abs tract form the contents of over 600 ar ticles relating to Track Train Dynamics (TTD ) , including an ex tensive thesaurus and key word index . Reedy , c. E. , and Phillips , E. A. , "Final Phase 09 Repor t on Tanks , Fittings , and Attachments in the Mechanical Environment of Accidents ," RPI-AAR Railroad Tank Car Safety Research and Tes t Proj ect , Report No. 09-1-24, February 1973. In this report, the failures of various parts of tank cars are examined and recommendations for improved designs are promoted. Stresses on stub sills and other body parts are calculated . Accidents involving tank car spills are lis ted and failed components identified. Eilber , R. J. , Maxey , t� . A. , and Duffy, A. R. , "Phase 12 Report on Analys is of Fracture Behavior of Tank Cars in Accidents ," RPI-AAR Railroad Tank Car Research an d Test Proj ect , Report No. RA-12-2-20 , September 1972. A summary of tank cars which have been involved in accidents is presented and categorized by the cause of crack initiation . In addition, each category is subdivided into five types of fracture behavior. The nature and origin of tank cracks are discussed in the context of proposed car modifications . Wes tin , R. A. , "Phase 02 on Dollar Loss Due to Exposure of Loaded Tank Cars to Fires--1975 through 1970," RPI-AAR Railroad Tank Car Safety Research Proj ect, Re port No. RA-02-l-l0 , Augus t 1972. The purpose of the study is to es timate the maximum probable savings wh ich migh t be realized by preventing fire damage to loaded tank cars . Data on 3840 damaged cars are used as a base . The benefits are estimated by assuming the installation of various protective systems to be 100% effective. The costs of such systems were then used in a cost-benefit analysis . A-30 RPI/AM Railroad Tank Car Safety Research and Test Proj ect , "Final Phase 02 Report Accident Analysis ," Report No . RA-02-2-18, . on August 1972. This report provides a summary of tank car accidents and 1% waybills for the period 1965-1970 . From the data, estimates of probabilities for accidents and the expected cos t of such accidents are derived. These estimates lead to cost-benefit analyses for a number of proposed car modifications . Sims, R. D. , and Phillips , E� A. , "Final Phase 10 Report on Couplers and Truck Securement," RPI-AAR Railroad Tank Car Safety Research and Tes t Project , Report No . RA-10-2-19 , Augus t 1972. Trucks and couplers have been identified as the mos t frequent causes of tank puncture. The pros and cons of modification to th ese components are evaluated. Ph illips , E. A. , et aL. , "Final Phase 05 Report on Tank Car Head Study, II RPI-AAR Railroad Tank Car Safety Research and Test Project, Report No . RA-05-1-17, July 1972. In this report are presented a number of recommended tank alterations and their cost-benefit analyses . Also documented are the preliminary tes ts performed on scale models and an analysis of scale model laws to es tablish the feas ib ility of such tests . Wes tin, R. A. , and Phillips, E. A., "Phase 01 Report on SlUIlmary of Rup tured Tank Cars Involved in Past Accidents," RPI-AAR Railroad Tank Car Safety Research an d Tes t Program, Report No . RA-01-2-7, July 1972 . In this report, the punctures and ruptures of tank cars invo lved in maj or accidents from 1958 to 19 72 are examined and described. Drawings are used to show the location , nature, and extent of damage to a number of tank cars , and the mechanisms causing failure are identified. A tabulation of car types , construction , cargo, and other characteristics is provided. RPI/AAR Tank Car Safety Research and Tes t Proj ect, "Final Phase 01 Report on Accident Review," Report No . RA- 10-4-16, June 19 72. The Phase 01 Report s ummarizes and cata10ges tank car accidents from 1965 through 1970 . Methods used for gathering and cataloging data are described. Data access codes and copies of the computer programs used to maintain the tape files are . also included in this report. A-31 RP I/AAR Railroad Tank Car Safety Research and Test Project, "Project Background, Scope, Plan , and Progress, April 1972. Th is paper documents the causes leading to the RPI-AAR effort and outlines the work to be done under each of 11 phases. Sims , R. D. , and Phillips, E. A. , "Phase 10 Report on Determination of Momen t Characteristics in a Horizontal Plane of Mated Combinations of Types "E" and "F" Couplers ," RPI-AAR Railroad Tank Car Safety Res earch and Test Project, Report No. RA-lO-l-ll, February 1972. Laboratory tests were performed on ma ted "E" and "F" couplers to determine the horizontal angles and moments at which separation or permanen t deformation takes place. The tes ts show the same magnitude of lateral resis tance for all comb i nations of tes ted couplers . Ph otographs document test procedures. Yang , T. H ., and �Ianos , W. P. , "Phase 08 Report on Computer Derailment Study, RPI-AAR Railroad Tank Car Safety Research and Test Project, Report II No. RA-0 8- l-l2, February 19 72 . A mathematical model is set forth to describe the motions, forces and accelerations experienced by derailing cars of a train . One objective of the exercise is to evaluate new car designs an d to relate train makeup to derailment severity. Re edy, C. E., and Phillips , E. A. , "Phase 01 Report on Sequence of Events Following Crescent City Derailment, RPI-AAR Railroad Tank Car Safety Research an d Tes t Program, ReII port No. RA-Ol-l-l, Augus t 19 70 . This report contains a brief but concis e synopsis of the events of the Crescent City conflagration . Of particular use is a series of sketches depicting the location and orientation of train cars and car fragments . AAR/RPI Railroad Tank Car Safety Research and Tes t Project, "Summary of Ruptured Tank Cars Involved in Pas t Accidents ," Report No. RA-01-2-3 (Phase 01) , Decemb er 1970 . Detailed data for 72 ruptured tank cars are presented, covering the period from 1958 to 1970 . Two ruptures involved brittle fractures , 6 were ethylene oxide cars , 64 cars burst violently. Th e 28 accidents lolere listed chronologically and the 64 cars were categorized by type , safety valve setting, design, insulation , and capacity. A-32 ADDITIONAL REFERENCES RPI/AAR Railroad Tank Car Safety Research and Test Project, "Dynamic Simulation of Freight Car and Lading during Impact," R-249 , November 1976. RPI/AAR Railroad Tank Car Safety Research and Test Proj ect, "Full-Scale Fire Test," Report No. RA-11-6-3l--Phase 11, December 1975. RPI/AAR Railroad Tank Car Safety Research and Test Proj ect , "Haterial Study on Steels Used in Current and Former Tank Car Construction and from Cars Involved in Accidents," Report No. RA-03-5-33- Final Phase 03 , August 1975. RPI /AAR Railroad Tank Car Safety Research and Test Proj ect , "Track Train Dynamics Report--Proceedings from the Second Track--Train Dynamics Seminar Held in Chicago in December 1974." Two Volumes , R- 176 and R-l77. RPI/AAR Railroad Tank Car Safety Research and Test Proj ect, "An Introduction to the Fracture Mechanics of Railroad Materials ," Report No . R-157, Hay 19 74. RPI/AAR Railroad Tank Car Safety Research and Test Proj ect, "Phase 11 Report on Analysis of 1/5 Scale Fire Tests," December 12 , 1973. RPI /AAR Railroad Tank Car Safety Research and Test Proj ect , "The Fracture Properties of Two Failed Cast Steel Wheels from the Union Pacific Railroad , R-123, May 1973. RPI/AAR Railroad Tank Car Safety Research and Tes t Proj ect, "Phase 12 Report on Tentative Tank Car Accident Investigation Guide," Report No. RA-12-l-6, April 1973. RPI/AAR Railroad Tank Car Safety Research and Test Project, "Phase 12 Report on Analysis of Tank Car Tub Rocketing in Accidents, Repor t No. RA-12-2-23, December 1972. RPI/AAR Railroad Tank Car Safety Research and Test Proj ect, "Overall Proj ect S ummary Report ," Report No. RA- OO-1-22, Oc tober 1972. RPI/AAR Railroad Tank Car Safety Research and Tes t Project, "Statistical Summary of Joint AAR-Railroad Survey of Cracked or Broken Couplers , Knuckles and Yokes in Freight Service on Five Railroads--lO Week Summer Period-June 1, 1971 through Augus t 7, 1971--4 Week Winter Period--January 15 , 1972 through February 14, 19 72," R-118 , Technical Report No. 3, September 1972. A-33 RPI /AAR Rai lroad Tank Car Safety Research and Freight Car Test Proj ect, "Summary of Visual Inspection Results Cracked or Broken Freight Car Couplers , Knuckles and Yokes--1097 Components Collected by 5 Railroads , R-117 , January 15 to February 15, 19 72, Technical Report No. 2, August 1972. �IIAAR Ra ilroad Tank Car Safety Research and Test Proj ect, . "Phase 11 Preliminary Report on Laboratory Fire Test Apparatus for Evaluating Thermal Shield Materials ," RA-11-3-15 , May 19 72 . RPl/AAR Railroad Tank Car Safety Research and Test Proj ect , "Analysis of 115 Scale Fire Test Data," Report No. RA-11-2-14 (Phase 11) , April 1972. RPl/AAR Rai lroad Tank Car Safety Research and Test Proj ect, "Phase 01 Report on Sequence of Events Following Hous ton, Texas Derailment," Report No. RA-01- 3-9 , October 1971. RPI/AAR Rai lroad Tank Car Safety Research and Test Proj ect, "Phase 04 Report Review of Literature and Re lated Experience," RA-04-1-8, July 30 , 1971. RPI/AAR Railroad Tank Car Safety Research and Test Project, "Phase 11 Report on Effects of Fire on LPG Tank Cars ," Report No . RA- l1-l-5 , Ap ril 1971. RPl/AAR Railroad Tank Car Safety Research and Test Project, "Track Train Dynamics to Improve Freight Train Performance through Train Handling, Train Hakeup , Track and Structure Consideration and Engineering Training (in combination with R-1S3) ," Report No . R- 122, 1970. A-34 5. Mi scellaneous Allen, E. to] . , "Transportation Systems Center Bibliography of Technical Reports ; July 1970-December 1976," DOT/TSC, Cambridge , Mass . Report No . DOT-TSC-OST-77-l7 , March 1978. This bib liography lists unlimited distribution reports released by the Transportation Systems Center from July 1970 through December 1976. Reports are listed by sponsoring agency , and are indexed by subject, personal author , corporate author, title, contract number , and report number. Gay , W. F. , "Transportation Safety Information Report, January , February , March 1977 ," DOT/TSC , Cambridge, Mas s ., for DOT/OST, Washington , D.C. , Final Report No . NTISUB/C/244-00l, June 1977 . Published quarterly , this report is a compendium of selected national-level transportation safety statistics for all modes of transportation. Each quarterly report represents and compares transportation fa talities , accidents , and injuries on a monthly and quarterly basis for the current and preceding year. In addition , it provides an overview of modal safety hazards , safety programs , and related accident prevention information . Tap , R. , and Kaprelian, A. , "Transporta tion Statistical Da ta and Informa tion," DOT/TSC, Cambrid�e , Mass., for DOT/OST, Washington, D.C. , Final Report No. DOT-TSC-OST-76-60, June 1977. The document contains an extensive review of in ternal and external sources of transpor tation data and statistics especial ly created for data administrators. Organized around the transportation industry and around the elements of the U.S. Department of Transportation , it is the most comprehen sive single document that reviews transportation data and its history . Petracek, S. J. , et al. , "Railroad Classification Yard Technology ," Stanford Research Institute, Menlo Park, California, for DOT/FRA Office of R&D , Final Report No. FRA-ORD-76/304 , January 1977. The major objective of this study was the identification of research and development necessary for technological improve ments in railroad classification yards . This involved a pro jection of future classification yard needs and a comparison of the requirements of existing technology . Separate tasks included a description of the hardware, costs , performance characteristics , and operational practices of existing yards ; formulation of general yard-network interaction concepts; A-35 collection of in-depth background information concerning the yard population in the United States (categorized by type , technology , and function) ; estimation of the demands likely to be placed on the nation's network of freight-car terminals during the foreseeable future ; and an assessment and prioritiza tion of those areas of terminal operations that warrant further research or development . Renzi, A. N. , "A Survey of Test Methods Currently Used for Simulating the Transportation Environment ," General American Transportation Corporation , Research Division , Niles , Illinois , for DOT/OHM, Washington, D.C. , Final Report , Contract No. DOT-OS-00038 , Ap ril 1978 . This is the final report of a survey study of the testing methods and practices currently employed for package evaluation . The package environmen t is separated into three distinct phases : transporta tion , storage, and handling. The maj or test methods intended for the environmental hazards principal to each phase are summarized, discussed , and wh ere possible , evaluated. A set of recommended interim test procedures , drawn basically from the existing methods , is presented . A-36 APPENDIX B MODELS FOR GENERATING PROBABILITY DISTRIBUTION FOR niE NUMBER OF CARS RELEASING AND THE AMOUNT RELEASED B.l INTRODUCTION In addition to the models for estimating parameters of probab il ity, distributions used in Chapters 4, 8, 9 and 10 , models were developed for estimating in detail the probability dist ributions of the number of cars releasing and the amount released . These models are based on explic it probability distributions for each probab ilistic factor involved in the event of a release . These factors include train velocity; the number of cars derailing , given the velocity; the number of hazardous-material cars derailing, given the total number of cars derailing ; the numb er of hazardous-material cars releasing, given the number derailing ; and the amount released, given the number releasing . Several numerical examples were developed using these models . Whereas the "parameter models" are useful for general scenarios, the "distribution models" are useful for mo re specific scenarios that are not covered by the parameter models. The most important example of this type of application is the situation in which both the total number of cars on the train and the number of cars carrying a hazardous material are specified. It might be of interest, in this situation , to determine the potential risk due to a train of a given size carrying a given amount of hazardous mater ial . Computerized distribution models can be used for this purpose. The heart of the distribution mo del is the probabil ity distribution of th e numb er of hazardous�aterial cars derailing as a function of the total numb er of cars derailing . In this situation , where the total number of haza,rdous-material cars is un spec ified , but the expected frequency is specified , the distribution is based on a simple binomial distribution with the following parameters : B-1 o The total number of cars derailing; and o The expec ted frequency of hazardous-material cars. For the case wh er e the number of hazardous-material cars on the train and the total numb er of cars on the train are specified , the distribution governing the number of hazardous ma terials derailing is based on a hyper geometric distribution . For both of these cases, the distributions are complicated by the assumption that the hazardous-material cars are blocked , the size of the blocks being an input parameter . These distri but ions are discussed in Section B.3 It should be noted that, in applying the hyper geometric model , the historical ag gregated dist ribution for the number of cars derailing as a function of speed may not be valid. Figure B-1 shows the relationship of the average numb er of cars derailing for mainline accidents as a func tion of both speed and the total number of cars in the train . NT' The figure shows that for train lengths of approximately 26 cars and lenger , the distribution of the number of cars derailing as a func tion of speed may be approximately independent of train length. Thus, when us ing the hypergeometric model, together with an assumed train length and the historical data for the dis tribution of the numb er of cars derailing, one is implicitly assuming that the train length is 26 cars or longer . Even with this stipulation , however , the relation is only approximate. Section B.2 presents the logical flow of the various parts of the computerized package that was developed to facilita te use of the distri but ion models . Sec tion B.3 discusses the distribution of the number of hazardous material cars derailing , given the total numb er of cars derail ing , and Section B.4 presents some examp les . B.2 LOGICAL FLOW OF COHPUTERIZED ANALYSIS PACKAGE The complete set of programs in the distribution model treats the various phases of the probabilistic processes in the following manner : B-2 14 c 100-150 : , II 76 - 100 NT f / NT 13 • ., ·75 i. ' / NT .... . j �. . I 12 . . .. ! / . . -...... 1 / / " f;:...... 11 ./ //,- 2 1 0,10 11 ·20 21 -30 31 ·40 41 ·50 51 61 ·70 SO >SO -60 71 · Range SPited FIGURE tn AS A FUNCTION OF DERAILMENT SPEED. V. AND TRAIN LENGTH. N B-1. Nn T • The joint distribution of the number of cars derailing and the velocity is given as an input matrix . • The distribution of the number of hazardous-material cars derailing as a func tion of the number of cars derailing is based on assumed block size and either a hypergeome tric or binomial distribution. (The details of these distributions are presented in Sec tion B.3.) • The distribution of the number of hazardous-material cars releasing as a func tion of the numb er of hazardous-material cars derail ing is assumed to be a binomial distribution with parameter q(v) where v is the velocity classification given in an input vector. The functional form of this binomial distribution is as follows : PROB (N R = n! k n-k (B-1) q(v) (1 - q(v» , = k! (n -k) ! where = number of hazardous-material cars releasing, and NR \ N number of hazardous-ma terial cars derailing. HD = • The dist ribut ion of the amount released, given the numb er of cars derailing , is assumed to be the sum of the amounts released per car . The amounts released per car are assumed to be independent, identically distributed random variables . The distribution of the amount released per car is based on historical data discussed previously. Th e logical flow of the synthesized computer mo dels and the nec essary inputs are depic ted in Figure B-2 . The interaction of some of the models can be described as follows: �-4 RUN P = Frequency of HazMat Cars q = pr (release/deraill N No. of HazMat Cars Derailed HD = N = No. of Cars Derailed O N No. of HazMat Cars Releasing R = A :::: Total Amount Released R FCN CUMDIST FIGURE B-2 . LOGICAL FLOW OF COMPUTERIZED DISTRIBUTION MODEL B-S • RL� takes a set of ND values (which have a joint probability mass func tion [PMF] with velocity) , together with either p or N , and produces a probability distribution of N for each H HD value of N D , based on the distributions presented in Section B.3. • FCN uses the output of RUN , a set of q(v) values , and the joint density of N and q(v) to produce a single distribut ion o for the number of hazardous-material cars rel easing . Th is func tion assumes that , as noted , the numb er of cars releasing is binomially dist ributed with parameter q(v) and N , and HD it combines this result with the density function for each �HD dist ribution, given q and ND• Thus : (N q, N ) = p = j) (N l q, N N = (B-2) P R D P R O ' � Lj j) and l � p (N ) = (N l q, N ) p (q = i, N = j). (B-3) R P R D O Li jL Cu�IST takes the dist ribution for N and mixes it with the • R semi-empirical distributions of amount re leased, given N , R to form an amount-released distribution . It is assumed that th e releases in all other cars, so that the n�fold convolution of the distribution of the amount released per car represents the distribution of the amo unt released per car from n cars. For n � 13, the convolutions are numerically computed. For n � 14 , the n-fold convolution is assumed to be normally distributed (central limit theorem) . (See for example, Figure B-3 .) Examples of the output of the compu terized package are presented in Section B.4. B-6 0.025 ..... Points on Convolution 0.02 0.015 Probability 0.01 � I ...... 0.005 o '...... ----- I I 80I 16I 0 240 o Thousands of Gallons Released by 11 Ca rs (Bins of Wid1h 2000) FIGURE 8--3. ELEVEN·FOI.D CONVOLUTION OF AMOUNT RELEASED PER CAR B.3 HODEL FOR EVALUAT ING THE PROBABILITY DI STRIBUTION MAOFTHENAT,NH , 'GICIVENAL N (THE NUMBER OF HAZARDOUS -MATERIAL DERAILING , D D GIVEN THE TOTAL NUMBER OF CARS DE RAILING) CARS The most importan t form of the distribution model can be applied to a specific scenario t.,hen the total number of cars and the total numb er of hazardous-ma terial cars on a particular train are specified . If the hazardous-material cars are distributed randomly throughout the consist , then the hypergeometric probability distribution can be used to deter mine the numb er of ha zardous-material cars derailing, given the total number of cars derailing . If th e hazardous-ma terial cars are blocked in one or more blocks , then the distribut ion can still be us ed on a hypergeometric distribution (of th e numb er of blocks) . Thus, most of the models in this section can be viewed as deriva tives of the hyper geometric distribution. Th e hypergeometric distribution is appropriate t..rhen the numb er of hazardous-material cars on the train is given . Th ere are other situat ions that might occur, however . When the numb er of hazardous-material cars is unrestricted and each car contains hazardous materials with a certain probability , then a binomial distribution is appropriat e. In addition, the hazardous-ma terial cars on the train may be blocked together . As a re sult of these other cons iderations , we can utilize the following general mo del to determine the number of hazardous-material cars derajled: 1. The train is subdivided into blocks of length G and each H block is either "hazardous materials" or "non-hazardous materials" in dependent of other blocks. Note that this type of model handles the situation in wh ich cars are located randomly (G 1) , as well as the situation where H = all the hazardous-material cars are blocked (G N ). H = H In addition , there are several intermediate ty pes of situations . 2. The number of hazardous-material blocks of cars is either binomial (as the total number of hazardous-material blocks is unrestric ted) or hypergeom etric (the numb er of hazardous material blocks is assumed) . B-a For any given situation, one can compute the number of hazardous material cars derailed from the numb er of hazardous-material blocks derailed. The total number of blocks derailed depends on the total numb er of cars derailed, as ·well as the location within the first block of the first derailing car. This is a somewhat involved problem in combinatorial mathemat ics and , in addition, on e or two of the derail ing blocks may be incomplete (for example , only one of the cars in the block might be derailing) . All of the possible cases were carefully examined and formulas developed for the numb er of hazardous-material cars derailing . Th e formulas will use a form of th e hypergeometric or binomial distribution . For convenience, the un derlying distribution of th e number of hazardous material blocks' derailing is denoted by g. For the two cases , expressions for g are as follows: c! , b! (a - b) (a - c) ! (B-4) g(a, b, c, y) = I - - (c y) 1 y ! (b y) I a ! (a - b - c + y) 1 for N given ; (Hypergeometric) H and bl g(a, b, c, y) = (8-5) y l (b - y) ! (Binominal) for N no t given . H In general: a = number of blocks; b = number of blocks derailing; c = numb er of hazardous-material blocks on train, if given; and y = number of hazardous-material blocks derailing . B-9 The algorithm for computing the probability distribution of the number of hazardous-material cars derailing is desc ribed below. In th e formula that fo llow, x represents the number of hazardous material cars derailing . In developing thes e formulas, the following lo gic was us ed. In any derailment , ther e will generally be n blocks of cars derailing where n is defined in th e algorithm. Of these blocks , n 2 will be of length - G and the other two will be shorter or equal to G and must be handled H H separately. Th e start of the derailment can occur in any one of G H locations within th e first derailing blocks . Th is location de te rmines th e size of the two blocks not equal to length G and the possibilities H of the total numb er of cars derailing . As an example, if th e derailment starts at G 1 location from th e start of the first derailing block, H - one can ob tain a value of x = 1 for the number of hazardous-material cars de railing , if the first block is the hazardous-mater ial block and all the other derailing blocks are non-hazardous materials . Thus, for each situation and for each location of the start of the derailment, what possib il it ies could occur if 0, 1, or 2 of the different size derailing blocks of materials were hazardous-material blocks were computed . The algo rithm for computing the distribut ion of x, P (x , is as ) follows : • If NO = (8-6) P(x) • 9 (G:T • I. . X). B-IO > • If NO 1: Compute (where [] denotes smallest integer less than or equal to ): (B-7) (B-8) r N - (n - 2) G (B-9) = o H ' - r = N o n' GH (B-lO) h (x) (B-ll) l.. B-1l There are four cases (A through D) : Case A: r' S r < GH is neither a multiple of GH nor one more than a (NmulD tiple of GH) x x p (1 - \ (1 ) (x) = GHny GH(n - 1) (B-12) for 0, G , 2G , etc. x = H H P(x) (B-13) 1, ••..•. + for 2, 3, , r - 1, G 1, G + 2, etc. x = H H hZ(x)(h2(x) - 1) P(x) = n(n - 1) (B-14 ) + for x = r, GH r, 2GH + r, etc. B-12 Case B: x x x (x) = 1 - 1 _ + G n G (n - 1) p H H G (n 1), ( ) ( � _ ) (B-15) + :� for x = 0, G , 2G , etc. H H N H g n, h (x) , (B-16) ' 1 ( G'�TH GH ) for x = 1, •••, G 1, G 1, • •• H - H + B-13 Case C: r r G + 1 is one mo re than a multiple of G ) 1 < = H (��D H x x P{x) = 1 - 1 G n G (n 1» G - G n G (n - 1) ( : )(1 H - ) + ..1.H ( 2-H ) H 1� 1 x(x - + n{n - 1) {GH = l l) g n, H , (B-17) I , G� ' G� G ( H H : ) for 0 , G , 2G , etc . :< = H H Here if holds l , A I = (B-18) {A} { 0, otherwise h 2 I ( x) - 1 h _ ( X» P {x) = � 1 G G n ) n - Cl(:) + -H Hl N H I n , h (x) , (B-19) g G ' G ' I � CH H for x = 1, G + 1, 2 G 1, etc . and GH 1. H H + F h (x) 2 hl X» I P(x) =- 1 (B-20) GH ( : ) n - 1 for x 2 , G 1, G 2, etc . • .•., H - H + B-14 Case 0: is neither a multiple of G nor one more than a (NO H multiple of G ; the number of blocks derailing depends H on the start ing point ; e.g., if G 5 and 7, the H = No = numb er of blocks derailing can be 2 or 3) (G - x H N N x T H g G n - 1, ( H ' H ' H G G) (B-2l) for x G , 2G , etc . = 0, H H 2 h X) h (x) � 1 I T H P(x) = g n, h (B-22) - � n - 1 G • I � (1 ) C�' H (x) for x 1, 2, ••• r - 1, G 1, = , H + G - r 1 h (x) (h (x) - 1) N H + I 1 T H P(x) = . g , n - 1, h ( X» G -{(n - 1) - 2) G • I H (n ) CH GH ) r - 1 h (x) (h (x) - 1) N N 2 2 T H g n, h (X» + G (n) (n - 1) 2 H GH ' GH ' ( (contin) ued) B-lS 2 h h (x) 1 - 1 l 1, h (B-23 ) + (x) g ( n · G n - 1 ) n 2 N N 1 -H ( - GH T ' - GH ' (X») x = r, G + r, etc. for H 2 h1 (x) hZ(x) P(x) = 1 - g - 1, h (B- 24) ( n G ' • (n 1) n 2 ' 1 G ) N N H ( - - GTH H (X� = + 1, ....., GH 1, + r + 1, .... for x r - GH B-16 B.4 EXAMPLES OF DISTRIBUTION MODELS Example 1: Two examples of the use of the distribution models are presented in this section. In the first example, we assume that the block length is 1; that is , the hazardous mat erials are randomly distributed throughout the train. The number of hazardous-material cars is given , and thus the distribution of th e num ber of hazardous-material cars derailing is hypergeometric . For the example, we specify the following : o Mainline derailments Class 2 track v = 16-20 mph N 55 cars T � T = 6000 gross tons N (a) 5 H = (b) 10 (c) 15 (d) 20. That is, we will compute P(N ) for a train of 55 cars , with 5 hazardous R material cars; then for 10 hazardous-material cars , and so on . Let = the probability of a train derailment per mile for Class 2 track, proportional to train gross tonnage. From Chapter 3, the appropriate cons tan t of proportionality is -8 1.7 x 10 per gross ton-mile. For a train of 6000 gross tons traveling one mile on Class 2 mainline track, the probability of a train derailment per mile is: -8 6000 x 1 x 1. 7 x 10 (B-25) -4 1 = .02 x 10 B-17 Th e probab ility that the derailment speed is 16-20 mph is 0.19. The compu ter program for P(N = 0, 1, for a specified train R • N ) length and specified numb er of hazar••dous H -material cars can then (N ) (N ) be utilizeTd with P(N v) for the given speed range. H D l was stored in an array . Rel ease probab il ity for ma inline P(N lv) derailmentsD at 16-20 mph was equated to the empirically observed value of 0.26. The program outputs are shown in Table B-1 . For a fixed train length 55) , P(N 0, 1, is given for 5, 10, 15 , 20. (NT = R = • N ) N = The average numb er of cars releasi•• ngH and varianc e areH also given for each can now be determined. NH• P(NR) -4 1.02 10 [P from Eq. (B-25) ] = x A x 0.19 [P(V l6-20 i 2) ] = 1 = x 0.12 [from Table B-1 for = 5 and = 11 . NH NR Thus , -6 P{N 1) 2.3 10 R = = x If there are 10 hazardous -material cars in a train with 35 cars, then -6 P(N 1) 10 R = = 1.02 x x 0.19 x [From Table B-1 for la , N 1] . 0.2 = R = NH 8-18 TABLE B-l. EXANPLE OF OUTPUT OF DI STRIBUTION MODEL N 55 T = N 5 H = N Prob (N ) R R o 0.8572482E + 00 0.7484290E 00 1 0.1236413E + 00 o + 2 0.1997443E 00 0.1134764E - 01 1 + 3 0.7298226E - 03 2 0.3792014E - 01 4 0.2978739E - 04 3 0.6007895E - 02 5 0.5752541E - 06 4 0.8000010E - 03 5 0.8784710E - 04 Average 0.14865E + 00 = 6 0.7598733E - 05 Variance 0.15399E + 00 = 7 0.4878692E - 06 8 0.2151541E - 07 9 0.5751029E - 09 }I 55 10 0.6962698E - 11 T = N = 20 H Average = 0.29730E + 00 Variance '" 0.33241E 00 N Prob (N ) + R R o 0.5861856E + 00 1 0.2731214E + 00 2 0.9394431E - 01 3 N 55 0.2890730E - 01 T = 4 0.8106545E - 02 N ... 15 5 0.2103000E - 02 H N 6 0.4986254E - 03 R Prvb 7 (NR) 0.1055594E - 03 0.6596730E + 00 8 o 0.1948973E - 04 1 0.2459895E + 00 9 0.3078554E - 05 2 0.6713533E - 01 10 0.4096894E - 06 3 0.1602293E - 01 11 0.4532435E - 07 4 0.3404927E - 02 12 0.4113918E - 08 5 0.6463139E - 03 13 0.3019449E - 09 6 0.1071813E - 03 14 0.1761245E - 10 7 0.1507171E - 04 15 0.7986510E - 12 8 0.1746483E - 05 16 0.2733018E - 13 9 0.1624700E - 06 17 0.6763145E - 15 10 0.1181556E - 07 18 0.1131954E - 16 11 0.6509693E - 09 19 0.1135558E - 18 12 0.2603567E - 10 20 0.5100784E - 21 13 0.7078707E - 12 14 0.1161912E - 13 15 0.8627465E - 16 Average = 0.59459E + 00 Average = 0.44594E + 00 Variance ... 0.76247E + 00 Variance = 0.53523E + 00 B-19 Thus , -6 P(N = 3.8 x10 • R = 1) The mean and variance obtained from the parameter model formulas were compared with those derived from the distribution model, with the following input parameters : r = 0. 1, G 1 (:. m 1) , H = GH = E(v) = 18 (the midpoint of the speed range) , and 2 (E(v» "" 324 ; and, assuming that mainline derailments at 16-20 mph are distributed evenly over the speed range, then: 1 5 E(v • ) = 76 .54, and E( ) 326. i == The values of P for the different values are (for N 55) : NH T = P 5 .09 10 .18 15 .27 20 .36 A comparison of the results of this model with the parameter model is contained in Tables B-2 and B-3. Th e means are comparable , but since the hypergeometric distribution involves a lower variance than the binomial distribution , the variance of the parameter model is higher . B-20 TABLE B-2 . COHPARISON OF (N ) MEA...'I' R N Mean N Hean Difference H R �� '* Mean - Mean Model 1 Model 1 2 5 .14865 .13946 .00919 10 .29730 .27892 .01838 15 .44594 .41838 .02756 20 .59459 .55784 .03675 TABLE B-3. COMPARISON OF VAR(N ) R N Var (N ) Var(N ) Difference H R R Model 1 * Model ** (Var - var ) 1 2 5 .15399 .17989 - .02590 10 .33241 .38993 - .05752 15 .53523 .63011 - .09488 20 .7624:- .90044 -. 13797 *Model 1 is the distribution mo del presented in this Appendix. ,'c *}Io de1 2 is the model presented in Chapter 8. B-2! Example 2: In a second example, a derailment was analyzed assuming the historical distribution of puncture probabilities , velocities, and derailment lengths . Th e block length was assumed to be fou r. To analyze the effect of a maj or change in inputs , the binomial distri bution with a � value of 0.5 (for the probability of any car contents H being hazardous) was utilized for the number of hazardous-material cars derailing . Table B-4 presents the resulting distribution of the number of cars releasing and the amount released. B.5 SUNHARY OF INPlITS ANO OUTPUTS FOR THE OISTRIBlITION HOOELS The inputs to the models inc lude : = fraction of all cars that carry hazardous material; or = numb er of hazardous-material cars and total cars in a train; set of q values for punc tu re probabilities (typically as a Afun ction of velocity) ; distribution for N (number of cars derailed) , typically as a A O function of velocity. OutPuts Includp. ! A distribution of the number of hazardous -material cars releasing ; and distribut ion of the amount of ha zardous materials released. A B-22 TABLE B-4. PROBABILITY DISTRIBUTIONS ASSU}tING liH = 0.5 Distribution of Numb er of Distribution of Amount Released Cars Releasing (gal. ) X P X P X) = X) So (NR (Aa 0 .6450 1000 .730902 1 .2026 5000 .759942 2 .0806 9000 .792304 3 .0366 15000 .839248 4 . 0179 19000 .861009 5 . 0090 25000 .895453 6 . 0045 35000 .949913 7 .0021 45000 .970529 8 .0010 55000 .982561 9 . 0004 75000 .994365 10 .0002 95000 .998154 11 .0001 125000 .999642 12 . 0000 175000 .999935 225000 .999947 275000 .999947 B-23/B-24 APPENDIX C OVERVIEW OF HAZARD-ASSESSHENT MODELS C.I INTRODUCTION This appendix provides an overview of the hazard-assessment models utilized in this investigation. To avoid lengthy discussions , each model is describ ed simply in terms of its basic equations. Derivations, theory, major as sumptions , and other detailed attributes can be found in the references cited. It should be noted that the scope of th is study did not call for the developmen t of any new models . Nor did satisfaction of basic objectives always warrant utilization of those availab le models of the greatest com plexity . Rather, it will be seen tha t the specific models select ed for use are those which have either been traditionally utilized for a given purpose, or which provide answers of an accuracy comparable to that of other study elements. Each model is designated by a letter, by which this appendix may be cross-referenced to Figure 12 -3 , which shows the need for, and us e of, each model. C. 2 IGNITION PROBABILITY ESTIMATION MODEL (A) The purpose of an ignition probability estimation model is to provide an in dication of "when" a released volume of flallDllab le or comb usti ble material is likely to ignite (if ever) . This knowledge is important because the time of ignition can have considerable influence upon the sequence of events that follow a release and, consequently, upon the impact of the release to the public. When comp ressed gases are released, there are five major feasible scenarios to consider: 1. Immediate ignition of ven ting gases due to nearby ignition sources or those caused by the accident, flame jet forms ; C-l 2. No immediate ignition and vapor cloud travels downwind; later ignition caus es flash fire through cloud ; 3. Same as (2) ab ove , but ignition leads to de tonation; 4. Tank car BLEVE or othen�ise explodes; and 5. No ignition; impact is due to gas/vapor inhalation toxicity. Estimates of conditional probab ilities of ignition for the first an d fourth of these scenarios, as well as for scenarios in volving non-volatile liquids and solids , are presented in Chapter 12 of this report. For all other scenarios , the probability of ignition to any time after release is given by [Cl] : * t -n fa A(t) dt, (C-l) _ e P(t) = I Jo where 2 , n = density of ignition sources , number/km f = mean frequency of activation of ignition sources, activations /source/second , = frac tion of cloud area in flammable condition , dimens ionless , A(t) 2 = land area covered by cloud at time t, km , t = el apsed time from release , s, and P(t) = probab ility of cloud ignition by time t. * See references at the end of this Appendix. C-2 C. 3 Fl.AI.'1E JET }lO DEL (B) Reference [C2l presents a review of investigations dealing with the predictions of flame sizes for turbulent gas jets . Based on its findings , it suggests USe of the following equations to define the length of the flame : L K H T - f f (C-2) = (1 - C) � D C jc + M aT f 0 an d 1 C = � f 1 r + M [ a J where K a factor ( 5.3) which depends on the Froude number , f = : stoichiometric air-fue l ratio r = = �:�; �!�l � ,a = molecular weights of gas and air, respectively , f a moles of reactants for stoichiometric combustion , = moleS of products o = adiabatic flame temperature , K, o = amb ient temperature , K = diameter of hcle in tank , m, and L = desired flame length , m. The value for r is ob tained by balancing the chemical reaction equation for complete combustion. For methane , the procedure is demonstrated by : CH CO (2 3.76) N CO 2H 0 + (2 3.76) N 4 + 2 + x 2 � 2 + 2 x 2 (2 32) (2 3.76 28) r a X + x x 17.2 • 16 C-l The denominator is the weight of me thane wh ich reacts with the total weight of air shown in the numerator . The procedure is rather sel f-evident if it is noted that air contains 3. 76 moles of nitrogen for each mo le of oxygen. The value of ex is a simp le ratio 0 f the number of moles of reactants to the mo les of products . In the example , the ratio is : --3 = = 1. (Note: N no t counted .) ex 3 2 Since the flame forms a cone as it travels aw ay from its source , sub sequent radiation intensity estimates are facilitated by computation of the diameter of a cylindrical flame with equal volume to the cone . The suggested equation [Ref. C2 l for use is : D e L 2 e (C-4) � s -- sin e sec D = ec D 2 2 2 + whe re the desired equivalent cylindrical flame diameter , m, and D e = e = the angle at wh ich the cone spreads out. 20 Typ ical values for a are said to lie between 10 and degrees. Since it is not possible to define any precise value , a selection of 10 .7 degrees allows simplific3t ion of Equa tion (C-4) to : D L (C-S) e ::: 10 .6 D + The he at flux received by a "target" or "observer" from a flame is given by (Ref. C2). Q T + S , (C-6) = Fa T £ cr f C-4 where F = view factor between flame and target , c£ = target absorptivity , " = atmospheric transmissivity , e = flame emissivity , 204 cr = Stefan-Boltzamann constant, W/m - K , o T equivalent blackbody flame temperature , K, f = 2 Q = heat flux received by target, W/m , and 2 s = solar insolation at target, W/m • The view factor F can be es timated from an expression given on page 247 of Reference C4 for a con figuration involving a right circular cy linder and a vertical plane with a normal passing through the center of one end of the cylinder and perpendicular to th e axis of the cy linder. The expression is : 1 -1 F = -- tan 'lfD C D [ � J L A- 2D -1 A(D - 1) 1 -l + tan - - tan B(D + 1) + D D D 1 (C-7) 'If 1 lAB !hl J '..Th ere D = d/r, d = dis tance from target to center of cylinder, m, r = radius of cy linder, m, L = 1./r, 2- = leng th of cylinder, 2 2 A = (D + 1) + L , 2 2 _ B = (D 1) + L . The emissivity of a flame is generally [e2 l com puted from: -kd 1 - e -l where K(m ) is an emission coeffic� en t (also called the attenutation coefficient) and d is the char acteristic thic kness dimension of the fl ame C-s in meters . For an alcohol, the emissivity can be as low as 0.067. For other substances , it may approach a value of 1.0. Becaus e of a lack of readily availab le experimental data for most hazardous materials of in teres t, it is us ually neces sary to assume a value of 1.0 for the parameter, thus providing an elemen t of conservatism to the analysis. In applicat ion of the model , a prob lem was realized in that it was difficult to find appropriate flame temperature data for the hazardous materials of concern. Adiabatic flame temperatures in the literature were excessively high, yet generally available. Through comparison of results ob tained when adiabatic and measured flame temperatures for propane are used in th e model , it was , therefore, decided to utilize adiabatic flame tempera tures , an d to conservatively adj ust results by setting E to a value of 0.06 for all hazardous ma terials . In other wo rds , it was es timated th at ab out 6% of the energy available would be radiated from the flame wh en adiabatic flame temperatures are assured. -8 2 The S tefan-Bol tzamann constant has a value of 5.66 x 10 W/m _ OK. The absorp tivity of various objects can vary with reflective properties and color, and thus can also be conservatively as signed a value of 1.0. The radiation from the flame to surrounding objects will be partially attenuated by ab sorption and scattering along the in tervening path by water vapor, carbon dioxide , dus t, and aerosol par ticles. On a clear humid day , the maj or componen t of attenuation will be that due to water vapor. The transmissivity of water vapor can be calculated, given th e distance between the flame and th e receiving object, the t��perature of the flame, the receiver and the int ervening atmo sphere, and the relat ive humid ity. Spectral data [CIS ] and the mean path length are then used to determine T , the transmissivity at wave number �. Th e mean transmissivity is w given by: E dw 'w W 0 T avg = J� S�Ew dw 0 C-6 A where E is the emissive power of the source at the wave number w. w specialized an d complex solution to this eq uation was developed by Arthur D. Li ttle some time ago. It was utilized in this study to provide es timates of 1 as a function of distance from the flame and other variables. C.4 INSTANTANEOUS-SOURCE VAPOR DISPERSION MODEL (C) Concentrations at ground level for gas es or vapors released instan taneously at ground level are given [C2l by the poin t-source equation: 2m [ 2 2 (x - ut) C(:( ,y, t) exp - + ---L-. 1 = 3/2 2 2 (211') 0 0 0 2 0 2 0 I (C-8) x y z x y J where m = mass of gas or vapor released, kg. a ,a ,a variance of the Gaussian con centration profiles in x y z = the respective directions , m, x = dis tance from source in downwind centerline direction, m, y = crosswind distance from centerline, m, z = height in vertical direction , m, u = wind velocity, mis, t = elapsed time from spill , s, and 3 • C = concentration of vapor or gas in air , kg/m Graphs giving a and as a function of downwind distance x and y 3X atmospheric stab ility class can be found in [C2l, [CS], [C6], and other references. (The parame ter a is commonly assumed to equal a.) References x y CS and C6 additionally provide guidance on how to select the atmospheric stability class most pertinent to any given combination of wind and weather conditions. Evaluation of the area downwind that will experience a concentration at or above a specified level C * is facilitated by use ofan equation giving the width of the moving cloud associated with C * The appropriate expression , derived by manipulation of Equation (C-8) , is C-7 C max = 2 2 tn (C-9 ) w 0'y * J C wh ere W is the t., idth of the cloud at ground level and C is the contaminan t max concentration at the downwind centerline x distance at wh ich W is desired. ObViously, the selected level C * mus t be less than or equal to C in order max for th e expression to be valid. During the various computations, a limitation of th is approach can be partially resolved by us ing a downwind x value in Equation (C-8) that is de te rmined from Ref. C2 : x = x + 5D, (x' replaces x in Eq. (C-8» (C-lO) where D is the diameter of the source. This adjus tment helps to resolve the inconsis tency between the as sumpt ion of a point so urce and the possible actuality of a significant source size. C.5 VAPOR FLASH FIRE MODEL (D) In a numb er of studies, various researchers have attempted to deal with the problem of modeling the effects of a flash fire through a gaseous cloud or plume . Review of their results during the course of this effort led to the conclusion that there is no currently available model that is reasonable in all assumptions. Consequently , it was decided to apply an approach that is logical , somewhat conservative , and quite straight forward . Given the ground area encompassed by a flammable cloud or plume , as determined from Models C or J described herein, one can make the valid observation that ignition of the gas or vapor at any point will cause a broad flame front to pass through all parts of the affected area . For a spill of significant magnitude, this front is likely to be measured in tens of me ters of thickness. Obviously then, people caught in the cloud unprotected would have a very high probab ility of suffering lethal injuries and, for impact-assessmen t purposes , it can be assumed that th is probab ility is essentially 1.0. C-8 An observer or other "target" to the side of the cloud or plume will see a moving, probably rectangular flame front passing by at a speed dep endent on the wind velocity and other factors. At the worst , the radiation intensity experienced by the ob server would be given by Equation (C-6) with the view factor F given by: ' F y -1 , (C-11) t an 2 11 X l + ( ) + Y .I I wher e x = A/ c Y = B/c A = one-half the width of the flame front thickness , m, B = flame front height , m, C = distance between flame edge and vertical targets , m, and F = view factor, dimensionless. This expression for F is a slightly modified form of an equation given on pages 15-50 of Ref. C9 (for configuration #8) . Based on observations of flame front thickness in a burning plume of methane, "A" can be safely assigned a value of 20 me ters for a large cloud or plume . Although the value for "B" is virtually un determinab le, an estimate of 30 meters should prove conservative for most rel eases. Note: Application of the model described immediately above in test problems resulted in the conclusion that thermal radiation damage to resources outside the burning cloud or plume cannot be reasonably assessed at this time . In consequence, results of this model were not utilized in the finalized impact-assessment results. Rather , it was assumed that the basic conservatism of the analysis for flash fire damages within the burning cloud or plume fully accounts for these additional zones of impact. C-9 C. 6 DETONATION HODEL (E) Certain gases and vapors dispersed in air may detonate wh en their concentrations are within flammable limits and sufficient power is supplied to initiate the detonation reaction . Th e traditional method of evaluating the resulting blast wave characteristics involves : 1) Comparison of the en ergy released by a unit weight of vapor upon detonation with that of a unit weight of TNT; and 2) Utilization of extens ive data for TNT and scaling laws . Th e TNT yield equivalent to the detonation of a mass of gas or vapor dispersed in air is given by: w = (C-12) 2090 Btu/lb TNT ' where M = the mass of gas or vapor liberated , lb ., llH = ha zardous-material heat of combustion at cons tant pressure , Btu/lb ., f = fraction of hazardous ma terial ava ilable for de tonation , and w = the equivalent TNT yield, lb . Curve-fitting of the overpressure data given in Ref . C7 and C8 and application of traditional scaling laws allows derivation of simple, approximate relationships for the pea� overpressure, namely : 2.2 1/3 w l/3 = 1500 for r/w < , p p (,r ) 14 · 4 (C 13 1/3 - ) 1/3 = 180 (; for r/w r > 14 , where r = radial distance from detonation site , ft, w = TNTo equivalent, lb . , and peak overpressure at r, psi . Pp = C-IO Similarly , it is possible to utilize tabulated data (Ref . C8 ) to derive an expression for the impulse over a particular range of interest. An equation so derived is : 0.7 0.063 w r I =0 ( for 5 30) , (C-14) 1.1 < < r ---=1:-:'-=-3w where I is the impulse in units of psi-sec. The model is also applicable to solids and liquids that have the potential to detonate under certain conditions . Indeed, it is more applicable to such condensed-phase substances than for dispersed gases and vapors . C. 7 TANK CAR EXPLOSION MODEL (F) Under proper conditions, a tank car can undergo a boiling liquid expanding vapor explosion (BLEW) . The event is not an explosion in the sense that a severe blast wave is generated, but rather alludes to the formation of a massive fireball above the tank car. Reference C10 presents a model of fireball formation and combustion that requires knowledge of two generally unknown parameters for hazardous materials ; viz., "constant equivalence ratio" and a "constant entrain ment coefficient ." In addition, it presents experimental data from tests with methane, ethane, and propane, and favorably compares results with those predicted by the model. Since propane is the hazardous ma terial most notorious for BLEVE 's, and since Ref. C10 provides empirical formulas for assessing propane fireball characteristics, hazard assessment can be facilitated by us ing these formulas across-the-board for all hazardous materials having th e potential to BLEW . This is a generally conservative and reasonable ap.plication , given the severity of the typical incident involving propane . C-ll The maximum diameter (D) , rise height (Z) , and burnout time (t) for propane fireballs are functions of the initial volume (V) of fuel available. Expressions presented by the cited reference are : 1/3 D = 7. 708 (v) (C-lS) 1/ 3 Z = 12 .73 (v) (C-l6) 1/3 t g 0.28 (v) (C-l7) wh ere D and Z are in units of centimeters , v in cubic centimeters, and t in seconds . Assuming an optically thick flame, one can estimat e the maximum radiation intensity received by a target at distance r from the fireball from Equation (C-6) , us ing the following expression to es timate a value for the view factor F: 2 (D/ 2) F = 2 (C-1S) r Another phenomenon that may accompany a tank car explosion is "rocketing , " in which the tank tears circumferentially , forming two "tubs ," one of which may then rocket through the air due to the rapid combustion of its contents. Detailed studies of the impact of rocketing are not available . However, Arthur D. Little, Inc. , has prepared esti mates of the maximum ro cketing range , based on a study by Battelle Columbus Laboratories (Ref. C16) . The results are shown in Figure C-l. These estimates are conservative , since the ob served ro cketing distances have not exceeded about 60% of the values shown. The actual rocketing range will be a random variab le , dependent on such factors as the pro perties of the hazardous material, the length of the tub , the angle at which the tub takes off, and the diameter of the tank. Adequately detailed estimates of these factors are not available. We have therefore assumed a "typical" rocketing range of 300 meters . It is assumed that under the flight path of the tub , for a width of 10 me ters, people will C-l2 5000 ... 4000 - � ;; CC DOT 1 12A34OW Inner Dia 119" ... - 0 .�� Initial Temp 100 � 3000 - F � Vinyl Chloride a: E ; 'x � � 2000 1000 ______o � �______� ______� __ __ 10,000 �� ____-, o 20,000 30,000 40,000 50.000 Tank Capacity (gal) Source: Arthur D. Little, Inc., estimates. FIGURE C-l. TUB ROCKETING DISTANCE C-13 be injured and property damaged, due to the spillage of burning material . The lethal zone is taken to be the ac tual area of impacts of the tub . This is estimated to be the length of a tank times its width , or 2 20m x 3m or approximately 60m • C.B LIQUID FLASH MODEL (G) When a compressed liquefied gas is released to the atmosphere under pressure , a certain fraction of the liquid will immediately vaporize. Th e remaining material , because of the cooling effect produced, will remain as liquid until such time as it strikes a warmer surface (the ground) , where again an additional fraction will immediately vaporize. Any liquid which remains on the ground will then form a pool which will evaporate fairly rapidly . If the entire cargo is lost rapidly, a large distinct vapor cloud will travel downwind , followed by a considerably smaller plume of vapor evolving from the evaporating pool . The weight fraction of any specific liquid which vaporizes upon exit from a tank can be estimated from a simple energy balanc� yielding the expression : (C-l9) where C liquid heat capacity of the hazardous material, J/kgOK, v = A = heat of vaporization , J/kg , T b = normal boiling point , oK, T . = initial temperature of the stored liquid, oK, and l. f = the fraction of liquid that flashes. To "f" must be added the fraction which rapidly boils off as the cold liquid strikes the usually warmer ground, and an additional fraction associated with entrainment of liquid aerosols. Since an analytical approach is unavailable for estimation of these latter fractions , but it has been estimated that each subsequent vaporization process C-l4 in creases "fll by a factor ranging from 1. ° to 2.0, the total fraction of liquid which flashes can be reasonab ly well determined by multiplying the computed va lue for "fll in Equation (C-19) by 1. 5. C.9 POOL SIZE MODEL (H) It is virtually an impossib le task to accurately estimate the ground area that will be covered when a given amount of a liquid is released from a storage vessel and a particular location is not specified. Numerous factors such as soil porosity, slope of the ground , vegetation, presence of depressions, and viscosity of the fluid can all significantly affect the outcome. Yet some estimate of the exposed surface area is necessary for vapor dispersion as well as liquid pool burning model applications . In the vapor dispersion model, a pool diameter is used in Equation (C-lO) where it allows adjustment of downwind centerline x distances to ac count for limitations of the point-source assumption Inspection of the impact of the diameter upon final results indicates that larger pool diameters lead to slightly smaller hazard zone areas. Thus , it is conservative to underestimate the pool size. In the pool burning model, increasing pool diame ters provide increas ing flame heights and , consequently, increases in the thermal radiation flux received at any chosen location. Simultaneously , however, large pool sizes reduce the overall time to burnout, and lead to reductions in the total time-integrated radiation exposure at any location . These counteracting effects serve to reduce the influence of pool size upon final results. Given the substantial uncertainties associated with any rigorous analytical estimation approach for the pool size, it is cons idered reasonable for the purposes of this study to simply as sume that any amount , of spilled liqUid will spread to a mean pool depth of app rOXimately 3 em. The diameter of the pool can then be estimated from: \ D 2 33.3 v = I (C-20) I '/l' I I C-15 I i I where 3 v = the volume of liquid released, m , and D = the pool diameter, m. The pool diame ters predicted by this equation are intuitively seen to be of the correct order of magnitude . Spills of 30 , 000 gallons result in pools of 228 feet in diameter; those of 50 gallons in pools of 9.3 feet in diameter . C.IO POOL EVAPORATION RATE HODEL (I) The rate of vaporization of a liquid pool is a complex function of chemical and physical properties (both liquid and substra te) , heat transfer effec ts , and mass-transfer phenomena . Nevertheless, it is possible to obtain conservative estimates of vaporization rates in a fairly scraightforward fashion by assuming the liquid temperature to be a constant. In the case of low-boiling-point substances that have been cooled while flashing , the appropriate temperature for use would be the normal boiling point . Fo r all other cases , the am bient temperature wo uld be most repr esen tative . The bas iC equa tion for the model is Ref. CII: 2 (vaporization rate, kg/m - s) = C (C-21) m km ' wh ere C = the vapor density of the liquid at the appropriate temperature, kg/m3 , and k a coefficient described below, m/ s. m = To ob ta in a value of k , either of two routes are available: m employment of turbulent boundary layer theory for flow acros s a flat plate (Ref. CI2) , or use of an empirical formula given in Ref . CII. Both approaches give similar results which can be averaged for general applicat ion . The pertinent relationships are: C-16 -3 O.S -0.2 -O . 67 k 4 .05 x 10 U L Sc , (C-22) m = (turbulent boundary-lower theory) (C-23) (Ref. Cll) , where U = wind velocity, m/s L = latera� pool dimension , m, and Sc = the Schmidt number of the hazardous material, dimensionless . The Schmidt numb er is the ratio of the kinematic viscosity of the hazardous material to its diffusivity in air. The former is itself the ratio of the viscosity of the fluid to its density . The diffus ivity in air of the substance can be obtained from tabulated values in the literature or estimated using various analytical techniques. C.ll CONTINUOUS SOURCE VAPOR DISPERSION MODEL (J) Concentrations at ground level for gases or vapors released continuously at ground level are given by Ref. C2 the point source equation. [ 2 me 2 1 C(x,y) = exp :! I for x 2'11' U 2 <- Ut, a Y a z (1 (C-24) 2 y = for x Ut , > J wh ere mo st parameters are as defined for the instantaneous source vapor dispersion model (C) . The exception , m ' is the rate at wh ich gas or e va po r evolves from the source in units of kg/s o Thewidt h of the vapor plume is again given by Equation (C-9) . / I C-17 I ), I I I I C. l2 POOL BURNING HODEL (K) A correlation for the height of the flame from a burning liquid pool fire is given by Thomas [Ref. Cl3 ] and found to be appropriate for general use in Re f. C2 . The expression is : 0.61 L -D = 1 (C-25) p�a J where 2 m = the fuel burning ate f r , kg/m s , 3 ...."'a density of ai r, kg/m 2 g = acceleration due to gravity, mls , D ::: diameter of pool , m, and L = flame height , m. The parame ter m is round from the expression: t Y r m. = r (C-26) where = the regression rate of the fuel wh ile burning, mis , and 3 = the density of the liquid at its boiling point , kg/m . Welker and Sliepcevich (Ref.CI4) provide a correlation for estima ting the flame tilt angle from the vertical when the flame is subj ected to wind forces . As reported in Ref. C2 , the expression is : tan e (C-27) = 3.3 cos a C-lS wh ere D = pool diameter, m, u = wind velocity, mIs , 2 V kinematic visco sity of air, m Is a = 2 g = acceleration due to gravity, mls , = fuel vapor density at its boiling point, p g 3 air density, kg/m , and e = flame tilt angle from vertical radius. The angle can be explicitly derived by allowing TC to equal th e left side of Equation (C-27) and using the relation: -1 (C-28) = sin e ). Given the diameter of the burning pool from Model 4, and the flame height and tilt from this model, Equations (C-6) and (C-7) are applied to estimate distances from the flame associated with selected damage criteria. The procedure is analogous to the one utilized for Model B, with the added stipulation that it is necessary to crudely es timate the duration of burning (so that total exposures can be estimated as well as incident heat flux to a target). A useful equation fo r this latter task is : vol = A (C-29) I Yr I � where 3 vol = volume of liquid spilled, m , y = liquid regression rate while burning , mIs , \ 2 I A = I area of burning pool, m , and duration of fire, s. I} jI C-19 C. l3 FIRE HODEL--FLA.'1HABLE SOLIDS /SPECIAL HAZARDS (L) A variety of flammable solids can react with water to generate flammable/explosive gases such as acetylene and hydrogen. Ye t others may spontaneously ignite in air and/or burn with an in tensity well beyond that associated with any ordinary combustible material . Becaus e of the nature of these substances , the relative rarity of their release (only 86 spills recorded between 1971 through 1977) , and their limited potential to cause widespread injury or property destruc tion , little work has been done to date in developing models for hazard assessment . In consequence, it is necessary to employ some rather crude approaches for quantifying expecting hazards . Equation (C-6) is generally appropriate for estimating the thermal radiation intensity profile from a fire involving these materials , if the view Fac tor F can be estimated for an appropriate configuration of source and target. Since tall flames would be the exception ra ther than the rule, it is assumed that the source will resemole a vertical , rectangular "wall" when viewed from a distance . Hence , it is possible to utilize the view factor expression given by Equation (C-ll) . Lacking an y specific historical data upon wh ich to base estimates, th e parameter "All is asswned to be one-half the length of a typical railroad car (A � 12m) , while liB" is taken to be three times the width ( -2. 5m) of a typical car. Thus , the ov erall scenario calls for the overturning of a car on to its side , spillage of flammable solid , and subsequent ignition . C.14 FIRE MODEL--ORDINARY COMBUSTIBLES (M) Ordinary combustible materials in solid form are unlikely to cau se any significant or unusual impact upon ignition. Fires will tend to be smoky and severely limited in radiative aspects . In addition, their size will generally be limited in most envisionable scenarios . Thus , it is not considered to be a worthwhile effort to assess the rather min imal impact of such ordinary and common events. C-20 :-.E FERENCES Cl. Distrigas Corporation Filing� , U.S. Federal Power Commission Docket CP73-38, Exhibit 19 , 1974 . S C2 . Raj , P.P • K. , and Kalelkar , A. " "As sessment Models in Support 0 f the Hazard As sessment Handbook," U.S. Coast Guard CG-D-65-74 , NTIS AD 776617 , January 1974. C3. Hawthorne , l C4. Wiebelt, J .A. , "Engineering Radiation Heat Transfer ," Holt , Rinehart, and Winston , New York, August 1966. C5 . Slade , D.H. , ed ., "Meteorology and Atomic Energy ," U.S. Atomic Energy Commission, Division of Technical Information, July 1968 . C6 . Turner , D.B. , ''Workbook of Atmospheric Dispers ion Es timates ," EPA, Research Triangle Park , North Carolina. C7 . Zabetakis , M.G., "Safety with Cryogenic Fluids ," Plenum Press , New York , 1967. ca. Kinney , G.F. , "Explosive Shocks in Air ," The MacMillan Company , New York, 1962. C9. Rohsenolls , W.M. , and Hartnett , J.P. , ed.'s, "Handbook of Heat Transfer ," McGraw-Hill, New York, 1973. ClO . Fay , J.A. , and Lewis , D.H. , Jr., "Unsteady Burning of Unconfined Fuel Vapor Clouds , " Proceedings of the Sixteenth Symposium (International) on Combustion, MIT , Cambridge , Mass. , 1976. (Sponsored by the Combustion Institute, Pittsburgh , Penn.). I I Cll. Mackay , D. , and Matsugu , R. S. , "Evaporation Rates f Liquid Hydrocarbon I 0 Spills on Land and Water ," Canadian Journal of Chemical Engineering , i 1971, p. 434. ?�, C12. Sherwood , T.K. , et a1., "Mass Trans fer ," McGraw-Hill , New York , 1975, p. 201 . C D. Thomas , P.U. , "Fire S(lread in Wooden Cribs - Part UI : TIle Effect of Wind , " Fire Res . Note No. 600 , Fire Research Station, Boreham Wood , England , June 1965 . C14. Welker , J.R. , and Sliepovich . C.M. , "The Effect of Wind on Flames ," i I Technical Report No. 2, Contract OCD-OS-62-89 , University of Oklahoma )I Research Institute , Nprman , Oklahoma , November 1965. 1 I C-2l ClS. Lud,,,ig, C.G. , et a1 ., "Study on Exhaust Plume Radiation Prediction , If General Dynamics Corporation, NASA CR-61222, 1968. Cl6 . Railway Progress Institute/Association of American Railroads , "Analysis of Tank Car Tub Rocketing in Ac cidents," Railroad Tank Car Safety Research and Test Proj ect, Report No . RA-12-2-23 , October 1972. C-22 APPENDIX D APPLICATION OF HAZARD-ASSESSMENT �ODELS D .1 INTRODUCTION Appendix C describes the basic elements of the various hazard- assess men t models. Appendix D discusses how these models were applied to generate desired results within the scope an d resources of this study . Its contents are, therefore , essential to an understanding of the bases for the results , as well as their limitations . D. 2 SPILL QUANTITIES UTILIZED The overall analysis presented in this report utilizes specific ranges of spill quantities to collate and an alyze the accident record data base . The first seven of these ranges and the specific amounts generally util ized for impact assessment computations are lis ted below : Ran ge * Amoun t As sumed* 1 - 100 50 101 1,000 SSO 1,001 - 5,000 3,000 5,001 - 10 ,000 7 ,500 10 ,001 - 25 ,000 17,500 25 ,000 - 50 ,000 37 ,500 50 ,001 - 100 ,000 75,000 * All amoun ts in gallons . •� is evident , the midpoints of the ranges were used for both average and worst-case impact assessments. Thus , the first limitation of the analysis stems from a realization that the true means of the ranges , as would be de termined from a rigorous and thorough analysis of spill records , may differ from the approximate arithmetic ave rages shown above . Additionally , it is to be noted that the basic conservatism of worst-case results was J somewhat tempered by use of the midpoints instead of upper bounds of ranges . I , I D-l I D.3 ENVIRONHENTAL CONDIT IONS SPECIFIED For all assessments involving vapor-dispersion hazards , it was necessary to spe cify the atmospheric stab ility class and the wind velocity. To facili tate matters , the neutral stability class D was chosen as representa tive of ave rage condition� along wi th a wind ve locity of 4 mls (about 9 mph) . Both classes C and D we re reasonable choices , but D provided a greater degree of conservatism. For worst case conditions (an invers ion with slow, steady winds) , the obvious choices were stable class F and a wind ve locity of 1 mls (about 2.2 mp h) . A number of models required the amb ient air temperature . This was fixed at 20°C for all cases , again to facilitate the analys is . Although tempe rature effects are likely to be significant in the liquid flash and pool evaporation rate models, it was noted that : • Uncertainties in the flash model (in regards to aerosol formation and boiling in contact with the ground) are likely to overshadow the significance of the air temperature ; an d • The evaporation rate model is inheren tly conservative due to its constant temperature assump tion and the large pool size estima tes resulting from the pool size estimation model. Remaining environmental specifications included a relative humidity of 50% for es timating atmospheric transmissivity , and a wind velocity of zero for pool fire assessments . The first choice was considered reasonable fo r universal application ; the second has essentially no effect, on the average , upon the accuracy of resultant impact estimates . D.4 VAPOR DISPERSION IMPACl'S A computer program was developed for all impact assessments involving the dispersion of gases and vapors . Using the basic equat ions for instan taneo�� and continuous-source dispe rsion models . the program iterated to find the , aximum downwind extent and maximum width of the cloud or plume associated ... with each specified scenario and aibo r rne concentration. These dimensions were then used to develop estimates of impacted area magnitudes (assuming D-2 the footprints resembled ellipses or triangles , as appropriate) . For spills of liquids , the program first applied the liquid flash , pool size , and pool evaporation rate models to estimate the size and strength of the source . In such cases , assessments entailed individual consideration of the fraction of liquid that flashed (assuming an instan taneous re lease) and the fraction that evolved more slowly from the resul ting pool (assuming a continuous release) . Impact assessment results presented were those associated with the largest impacted areas . When the gases or vapors were flammable , it was necessary to incor porate the ignition probability model into the iterative process . This required two preliminary decisions : one dealing with the magnitudes of the ignition source densities to be assumed , and the other with the average probability at which a cloud or plume will ignite . Es timates for ignition source densities evolved from a rather crude evaluation of ignition sources in urban , suburban , and rural settings . For the product "nf" in the pertinent equation, results were : Setting Range'" Geometric Hean*- Urban 80 - 800 '" 250 Suburban 30 - 300 '" 100 Rural 3 - 30 '" 10 2 * All units are activations/km -s The me an s shown above were used for al l impact- as sessment purposes . The estimates have substantial un certainties , but mus t be considered reasonable for· use at this time, given the absence of a better approach . The program followed the growth of a cloud or a plume incrementally , and calculated the probab ility of ignition as a function of time . Areas affected by an ignition were then estimated by assuming ignition at prcb ab ilities between 0.45 and 0.55. I J A problem presented itself when the gases or vapors were simultaneously r flammab le and highly toxic, since ignition would preclude further dispers ion I , J , I I D-3 of toxic con taminants (assuming no similar effect from combustion products) . In such cases , im pact results for toxic clouds or plumes were manually adjus ted to account for ignition probabilities. Th is required calculation of the ratio of the downwind distance at which ignition was expected (with P = 0.45 to 0.55) an d the maximum downwind extent of hazard with no ignition , and then multiplication of this fraction by th e maximum impact area asso ciated with a given toxic concentration (again assuming no ignition) . Finally, it must be noted that a specialized subroutine Arthur D. Little de veloped a number of years ago was utilized for estimation of the dispersion parame ters and as a function of downwind distance. Developed with least cry crz squares regression techniques , the routine incorporates the graphically presented data in the references of Appendix C. D.5 FIRE IMPACTS Pool fire scenarios were addressed using a comb ination of the pool fire and pool size models , the latter assuming that all hazardous-materials released form a pool (i.e. , liquid is not allowed to flash) . Given specified damage criteria, a computer program searched the radiation flux profile* from the flame to find the associated separation distances an d, ultimately , the magnitudes of the im pacted areas. Where exposure times were necessary , it was as sumed that people would find shelter or run a sufficient distance from the fire within 30 seconds . Buildings, however, were allowed continuous exposure for the duration of the fire or a maximum of 1 hour (assuming th e presence of firefighting activities at or before this limit) . The procedures applied for flame jets ** and burning flammable solids were essentially identical. In the case of vapor-cloud flash fires, results from the vapor-dispersion analysis were used to define the area that would be engulfed in flames at the time and location of ignition. These areas were taken to represent those of potential lethality and building ignition. Because of in surmountable difficulties, the radiation flux profile from the moving flame front to an observer outside the cloud or plume could not be f fully evaluated, however. Thus, it was assumed that inj uries would not occur because of the necessarily brief radiation exposures associated with such events. 2 * Solar isolation assumed to be 150 Btu/hr-ft • **H ole size assumed to be 12 inches . The fireball impact-assessmen t procedure (for BLEVE effects) had three significan t features : • Tn e fireball was fixed at its maximum diameter at one-half its maximum height. • No limits were placed on human or property exposure times , since they could be estimated and tended to be brief. • Average impacts were evaluated by assuming that only half the cargo participates in fireball formation , whereas wo rs t case impacts assumed involvement by the entire cargo. 0. 6 EXPLOSION IMPACTS The equations presented for the vapor cloud detonation model (Appendix C) were rearranged to provide explicitly the radial distances associated with specified damage criteria. The fraction of hazardous materials available for detonation was conservatively assumed to be 7.5% for the average event and 15% for the worst-case event. Explosions involving other scenarios were addressed, assuming the en tire amount spilled was detonable. 0. 7 OTHER LIMITATIONS The major limitations of the impac t-assessment methodology should be listed for consideration as future developmental efforts. They are: 1. Vapor dispersion models assume neutrally buoyant vapors or gases; they may be non-conservative for many hazardous materials; excessively conservative for others. 2. Vapor-dispersion models assume flat open land . Buildings, trees, and other obstructions tend to enhance mixing, but lessen hazard extents . 3. Impact assessments for toxic vapor or gas releases do not rigorously consider the time/concentration effects upon humans . Damage criteria require refinement through comprehensive search and analysis of toxicological literature . i 0-5 I I I I 4. The pool size estimation model is rather arbitrary in nature . Pool size affects impact, bu t a realistic spreading model is unavailable. 5. Tank car rocketing is a potentially devastating event not addressable with current knowledge. 6. Poten tially toxic products of combustion were not addressed because of the considerab le effort required to do so. 7. The lists of representative hazardous materials for each category were derived from data for all hazardous-material spills . An analysis of railroad accidents alone may alter results. 8. The entire concept of using representative hazardous materials in the risk-assessment procedure has an adverse effect on the validity of the analysis . Considera tion should be given to chemical-specific impact assessment through automated means . 9. more rigorous treaOnen t of pool evaporation phenomena A may be warranted. 10 . The view factor estimation technique for pool fires can be improve d with additional effort. 11. The en tire subject area of ignition-source densities and ignition probabilities has never been treated well. Developmental work in this area might be worthwhile. 12 . Impact due to vapor flash fires warrants further investigation . 13. Th e emissive power of flames from different hazardous materials can be quantified better; some experimental work and/or an additional literature search might lead to a better understanding of impacts from open flames . 14. Ignition criteria for wood was based upon long-term exposure data. A need exists to better review short- term, high radiat ion-intensity effects. 0-6 15 . The analysis essen tially assumed that compressed liquefied gases were shipped at ambien t temperatures . Improvements are possible for those shipped in insulated or refrigerated cars at lower temperatures . 16. The hazards and impacts of hazardous solids, oxidizers , organic peroxides, and the like , have never been studied well . Mos t, if not all, work has been directed toward gases and liquids with common actions upon release. 17. The analysis did not consider explosives or radioactive materials. 18. Results of BLEVE model application were not always realistic. A more rigorous analysis involving the time-growth-rise history of the fireball is necessary. , I I I iJ 116 copies I D-7/D-8 u. s. GOVEIU'''lENf .�I"T Jl'G OFFICE : 1983--700-.'6--238 I * jI J II JI II if QI5i f If II I Ii i